Machine Learning (cs.LG)

Abstract: Offline reinforcement learning (RL) provides a promising solution to learning an agent fully relying on a data-driven paradigm. However, constrained by the limited quality of the offline dataset, its performance is often sub-optimal. Therefore, it is desired to further finetune the agent via extra online interactions before deployment. Unfortunately, offline-to-online RL can be challenging due to two main challenges: constrained exploratory behavior and state-action distribution shift. To this end, we propose a Simple Unified uNcertainty-Guided (SUNG) framework, which naturally unifies the solution to both challenges with the tool of uncertainty. Specifically, SUNG quantifies uncertainty via a VAE-based state-action visitation density estimator. To facilitate efficient exploration, SUNG presents a practical optimistic exploration strategy to select informative actions with both high value and high uncertainty. Moreover, SUNG develops an adaptive exploitation method by applying conservative offline RL objectives to high-uncertainty samples and standard online RL objectives to low-uncertainty samples to smoothly bridge offline and online stages. SUNG achieves state-of-the-art online finetuning performance when combined with different offline RL methods, across various environments and datasets in D4RL benchmark.

Abstract: We first elucidate various fundamental properties of optimal adversarial predictors: the structure of optimal adversarial convex predictors in terms of optimal adversarial zero-one predictors, bounds relating the adversarial convex loss to the adversarial zero-one loss, and the fact that continuous predictors can get arbitrarily close to the optimal adversarial error for both convex and zero-one losses. Applying these results along with new Rademacher complexity bounds for adversarial training near initialization, we prove that for general data distributions and perturbation sets, adversarial training on shallow networks with early stopping and an idealized optimal adversary is able to achieve optimal adversarial test error. By contrast, prior theoretical work either considered specialized data distributions or only provided training error guarantees.

Abstract: We study the problem of best-arm identification (BAI) in the fixed-budget setting with heterogeneous reward variances. We propose two variance-adaptive BAI algorithms for this setting: SHVar for known reward variances and SHAdaVar for unknown reward variances. Our algorithms rely on non-uniform budget allocations among the arms where the arms with higher reward variances are pulled more often than those with lower variances. The main algorithmic novelty is in the design of SHAdaVar, which allocates budget greedily based on overestimating the unknown reward variances. We bound probabilities of misidentifying the best arms in both SHVar and SHAdaVar. Our analyses rely on novel lower bounds on the number of pulls of an arm that do not require closed-form solutions to the budget allocation problem. Since one of our budget allocation problems is analogous to the optimal experiment design with unknown variances, we believe that our results are of a broad interest. Our experiments validate our theory, and show that SHVar and SHAdaVar outperform algorithms from prior works with analytical guarantees.

Abstract: We present Galactic, a large-scale simulation and reinforcement-learning (RL) framework for robotic mobile manipulation in indoor environments. Specifically, a Fetch robot (equipped with a mobile base, 7DoF arm, RGBD camera, egomotion, and onboard sensing) is spawned in a home environment and asked to rearrange objects - by navigating to an object, picking it up, navigating to a target location, and then placing the object at the target location. Galactic is fast. In terms of simulation speed (rendering + physics), Galactic achieves over 421,000 steps-per-second (SPS) on an 8-GPU node, which is 54x faster than Habitat 2.0 (7699 SPS). More importantly, Galactic was designed to optimize the entire rendering + physics + RL interplay since any bottleneck in the interplay slows down training. In terms of simulation+RL speed (rendering + physics + inference + learning), Galactic achieves over 108,000 SPS, which 88x faster than Habitat 2.0 (1243 SPS). These massive speed-ups not only drastically cut the wall-clock training time of existing experiments, but also unlock an unprecedented scale of new experiments. First, Galactic can train a mobile pick skill to >80% accuracy in under 16 minutes, a 100x speedup compared to the over 24 hours it takes to train the same skill in Habitat 2.0. Second, we use Galactic to perform the largest-scale experiment to date for rearrangement using 5B steps of experience in 46 hours, which is equivalent to 20 years of robot experience. This scaling results in a single neural network composed of task-agnostic components achieving 85% success in GeometricGoal rearrangement, compared to 0% success reported in Habitat 2.0 for the same approach. The code is available at github.com/facebookresearch/galactic.

Abstract: When using adversarial training, it is common practice to train against the most egregious failures. However, this might imply using examples with sensitive information (such as leaked passwords or security vulnerabilities) as training data. One might assume that language models trained with gradient descent never generate text snippets which were only present in examples associated with the lowest possible reward. In this paper, we show that this assumption is wrong: in some situations, large language models do learn from such negatively-reinforced examples. We present a specific training setup that enables Pythia-160M to generate passwords with a probability slightly greater than chance, despite only showing it these passwords on examples where the model is incentivized to not output these passwords. Our code is available at https://github.com/FabienRoger/Learning-From-Negative-Examples

Abstract: Recently, diffusion models have achieved remarkable performance in data generation, e.g., generating high-quality images. Nevertheless, chemistry molecules often have complex non-Euclidean spatial structures, with the behavior changing dynamically and unpredictably. Most existing diffusion models highly rely on computing the probability distribution, i.e., Gaussian distribution, in Euclidean space, which cannot capture internal non-Euclidean structures of molecules, especially the hierarchical structures of the implicit manifold surface represented by molecules. It has been observed that the complex hierarchical structures in hyperbolic embedding space become more prominent and easier to be captured. In order to leverage both the data generation power of diffusion models and the strong capability to extract complex geometric features of hyperbolic embedding, we propose to extend the diffusion model to hyperbolic manifolds for molecule generation, namely, Hyperbolic Graph Diffusion Model (HGDM). The proposed HGDM employs a hyperbolic variational autoencoder to generate the hyperbolic hidden representation of nodes and then a score-based hyperbolic graph neural network is used to learn the distribution in hyperbolic space. Numerical experimental results show that the proposed HGDM achieves higher performance on several molecular datasets, compared with state-of-the-art methods.

Abstract: We consider a cross-silo federated learning (FL) setting where a machine learning model with a fully connected first layer is trained between different clients and a central server using FedAvg, and where the aggregation step can be performed with secure aggregation (SA). We present SRATTA an attack relying only on aggregated models which, under realistic assumptions, (i) recovers data samples from the different clients, and (ii) groups data samples coming from the same client together. While sample recovery has already been explored in an FL setting, the ability to group samples per client, despite the use of SA, is novel. This poses a significant unforeseen security threat to FL and effectively breaks SA. We show that SRATTA is both theoretically grounded and can be used in practice on realistic models and datasets. We also propose counter-measures, and claim that clients should play an active role to guarantee their privacy during training.

Abstract: A large number of works aim to alleviate the impact of noise due to an underlying conventional assumption of the negative role of noise. However, some existing works show that the assumption does not always hold. In this paper, we investigate how to benefit the classical models by random noise under the framework of Positive-incentive Noise (Pi-Noise). Since the ideal objective of Pi-Noise is intractable, we propose to optimize its variational bound instead, namely variational Pi-Noise (VPN). With the variational inference, a VPN generator implemented by neural networks is designed for enhancing base models and simplifying the inference of base models, without changing the architecture of base models. Benefiting from the independent design of base models and VPN generators, the VPN generator can work with most existing models. From the experiments, it is shown that the proposed VPN generator can improve the base models. It is appealing that the trained variational VPN generator prefers to blur the irrelevant ingredients in complicated images, which meets our expectations.

Abstract: Temporal Graph Learning, which aims to model the time-evolving nature of graphs, has gained increasing attention and achieved remarkable performance recently. However, in reality, graph structures are often incomplete and noisy, which hinders temporal graph networks (TGNs) from learning informative representations. Graph contrastive learning uses data augmentation to generate plausible variations of existing data and learn robust representations. However, rule-based augmentation approaches may be suboptimal as they lack learnability and fail to leverage rich information from downstream tasks. To address these issues, we propose a Time-aware Graph Structure Learning (TGSL) approach via sequence prediction on temporal graphs, which learns better graph structures for downstream tasks through adding potential temporal edges. In particular, it predicts time-aware context embedding based on previously observed interactions and uses the Gumble-Top-K to select the closest candidate edges to this context embedding. Additionally, several candidate sampling strategies are proposed to ensure both efficiency and diversity. Furthermore, we jointly learn the graph structure and TGNs in an end-to-end manner and perform inference on the refined graph. Extensive experiments on temporal link prediction benchmarks demonstrate that TGSL yields significant gains for the popular TGNs such as TGAT and GraphMixer, and it outperforms other contrastive learning methods on temporal graphs. We will release the code in the future.

Abstract: Despite extraordinary progress, current machine learning systems have been shown to be brittle against adversarial examples: seemingly innocuous but carefully crafted perturbations of test examples that cause machine learning predictors to misclassify. Can we learn predictors robust to adversarial examples? and how? There has been much empirical interest in this contemporary challenge in machine learning, and in this thesis, we address it from a theoretical perspective. In this thesis, we explore what robustness properties can we hope to guarantee against adversarial examples and develop an understanding of how to algorithmically guarantee them. We illustrate the need to go beyond traditional approaches and principles such as empirical risk minimization and uniform convergence, and make contributions that can be categorized as follows: (1) introducing problem formulations capturing aspects of emerging practical challenges in robust learning, (2) designing new learning algorithms with provable robustness guarantees, and (3) characterizing the complexity of robust learning and fundamental limitations on the performance of any algorithm.

Abstract: We present a novel learning-based method that achieves state-of-the-art performance on several heart rate estimation benchmarks extracted from photoplethysmography signals (PPG). We consider the evolution of the heart rate in the context of a discrete-time stochastic process that we represent as a hidden Markov model. We derive a distribution over possible heart rate values for a given PPG signal window through a trained neural network. Using belief propagation, we incorporate the statistical distribution of heart rate changes to refine these estimates in a temporal context. From this, we obtain a quantized probability distribution over the range of possible heart rate values that captures a meaningful and well-calibrated estimate of the inherent predictive uncertainty. We show the robustness of our method on eight public datasets with three different cross-validation experiments.

Abstract: In this work, we addresses the problem of modeling distributions of graphs. We introduce the Vector-Quantized Graph Auto-Encoder (VQ-GAE), a permutation-equivariant discrete auto-encoder and designed to model the distribution of graphs. By exploiting the permutation-equivariance of graph neural networks (GNNs), our autoencoder circumvents the problem of the ordering of the graph representation. We leverage the capability of GNNs to capture local structures of graphs while employing vector-quantization to prevent the mapping of discrete objects to a continuous latent space. Furthermore, the use of autoregressive models enables us to capture the global structure of graphs via the latent representation. We evaluate our model on standard datasets used for graph generation and observe that it achieves excellent performance on some of the most salient evaluation metrics compared to the state-of-the-art.

Abstract: Deep learning (DL) models have seen increased attention for time series forecasting, yet the application on cyber-physical systems (CPS) is hindered by the lacking robustness of these methods. Thus, this study evaluates the robustness and generalization performance of DL architectures on multivariate time series data from CPS. Our investigation focuses on the models' ability to handle a range of perturbations, such as sensor faults and noise, and assesses their impact on overall performance. Furthermore, we test the generalization and transfer learning capabilities of these models by exposing them to out-of-distribution (OOD) samples. These include deviations from standard system operations, while the core dynamics of the underlying physical system are preserved. Additionally, we test how well the models respond to several data augmentation techniques, including added noise and time warping. Our experimental framework utilizes a simulated three-tank system, proposed as a novel benchmark for evaluating the robustness and generalization performance of DL algorithms in CPS data contexts. The findings reveal that certain DL model architectures and training techniques exhibit superior effectiveness in handling OOD samples and various perturbations. These insights have significant implications for the development of DL models that deliver reliable and robust performance in real-world CPS applications.

Abstract: Policy-based algorithms are among the most widely adopted techniques in model-free RL, thanks to their strong theoretical groundings and good properties in continuous action spaces. Unfortunately, these methods require precise and problem-specific hyperparameter tuning to achieve good performance, and tend to struggle when asked to accomplish a series of heterogeneous tasks. In particular, the selection of the step size has a crucial impact on their ability to learn a highly performing policy, affecting the speed and the stability of the training process, and often being the main culprit for poor results. In this paper, we tackle these issues with a Meta Reinforcement Learning approach, by introducing a new formulation, known as meta-MDP, that can be used to solve any hyperparameter selection problem in RL with contextual processes. After providing a theoretical Lipschitz bound to the difference of performance in different tasks, we adopt the proposed framework to train a batch RL algorithm to dynamically recommend the most adequate step size for different policies and tasks. In conclusion, we present an experimental campaign to show the advantages of selecting an adaptive learning rate in heterogeneous environments.

Abstract: Reinforcement learning (RL) has shown empirical success in various real world settings with complex models and large state-action spaces. The existing analytical results, however, typically focus on settings with a small number of state-actions or simple models such as linearly modeled state-action value functions. To derive RL policies that efficiently handle large state-action spaces with more general value functions, some recent works have considered nonlinear function approximation using kernel ridge regression. We propose $\pi$-KRVI, an optimistic modification of least-squares value iteration, when the state-action value function is represented by an RKHS. We prove the first order-optimal regret guarantees under a general setting. Our results show a significant polynomial in the number of episodes improvement over the state of the art. In particular, with highly non-smooth kernels (such as Neural Tangent kernel or some Mat\'ern kernels) the existing results lead to trivial (superlinear in the number of episodes) regret bounds. We show a sublinear regret bound that is order optimal in the case of Mat\'ern kernels where a lower bound on regret is known.

Abstract: Multi-agent reinforcement learning (MARL) addresses sequential decision-making problems with multiple agents, where each agent optimizes its own objective. In many real-world instances, the agents may not only want to optimize their objectives, but also ensure safe behavior. For example, in traffic routing, each car (agent) aims to reach its destination quickly (objective) while avoiding collisions (safety). Constrained Markov Games (CMGs) are a natural formalism for safe MARL problems, though generally intractable. In this work, we introduce and study Constrained Markov Potential Games (CMPGs), an important class of CMGs. We first show that a Nash policy for CMPGs can be found via constrained optimization. One tempting approach is to solve it by Lagrangian-based primal-dual methods. As we show, in contrast to the single-agent setting, however, CMPGs do not satisfy strong duality, rendering such approaches inapplicable and potentially unsafe. To solve the CMPG problem, we propose our algorithm Coordinate-Ascent for CMPGs (CA-CMPG), which provably converges to a Nash policy in tabular, finite-horizon CMPGs. Furthermore, we provide the first sample complexity bounds for learning Nash policies in unknown CMPGs, and, which under additional assumptions, guarantee safe exploration.

Abstract: We study the multi-fidelity multi-armed bandit (MF-MAB), an extension of the canonical multi-armed bandit (MAB) problem. MF-MAB allows each arm to be pulled with different costs (fidelities) and observation accuracy. We study both the best arm identification with fixed confidence (BAI) and the regret minimization objectives. For BAI, we present (a) a cost complexity lower bound, (b) an algorithmic framework with two alternative fidelity selection procedures, and (c) both procedures' cost complexity upper bounds. From both cost complexity bounds of MF-MAB, one can recover the standard sample complexity bounds of the classic (single-fidelity) MAB. For regret minimization of MF-MAB, we propose a new regret definition, prove its problem-independent regret lower bound $\Omega(K^{1/3}\Lambda^{2/3})$ and problem-dependent lower bound $\Omega(K\log \Lambda)$, where $K$ is the number of arms and $\Lambda$ is the decision budget in terms of cost, and devise an elimination-based algorithm whose worst-cost regret upper bound matches its corresponding lower bound up to some logarithmic terms and, whose problem-dependent bound matches its corresponding lower bound in terms of $\Lambda$.

Abstract: Post-hoc explanation techniques such as the well-established partial dependence plot (PDP), which investigates feature dependencies, are used in explainable artificial intelligence (XAI) to understand black-box machine learning models. While many real-world applications require dynamic models that constantly adapt over time and react to changes in the underlying distribution, XAI, so far, has primarily considered static learning environments, where models are trained in a batch mode and remain unchanged. We thus propose a novel model-agnostic XAI framework called incremental PDP (iPDP) that extends on the PDP to extract time-dependent feature effects in non-stationary learning environments. We formally analyze iPDP and show that it approximates a time-dependent variant of the PDP that properly reacts to real and virtual concept drift. The time-sensitivity of iPDP is controlled by a single smoothing parameter, which directly corresponds to the variance and the approximation error of iPDP in a static learning environment. We illustrate the efficacy of iPDP by showcasing an example application for drift detection and conducting multiple experiments on real-world and synthetic data sets and streams.

Abstract: Since 2014, artificial neural networks have been known to be vulnerable to adversarial attacks, which can fool the network into producing wrong or nonsensical outputs by making humanly imperceptible alterations to inputs. While defenses against adversarial attacks have been proposed, they usually involve retraining a new neural network from scratch, a costly task. In this work, I introduce the Finite Gaussian Neuron (FGN), a novel neuron architecture for artificial neural networks. My works aims to: - easily convert existing models to Finite Gaussian Neuron architecture, - while preserving the existing model's behavior on real data, - and offering resistance against adversarial attacks. I show that converted and retrained Finite Gaussian Neural Networks (FGNN) always have lower confidence (i.e., are not overconfident) in their predictions over randomized and Fast Gradient Sign Method adversarial images when compared to classical neural networks, while maintaining high accuracy and confidence over real MNIST images. To further validate the capacity of Finite Gaussian Neurons to protect from adversarial attacks, I compare the behavior of FGNs to that of Bayesian Neural Networks against both randomized and adversarial images, and show how the behavior of the two architectures differs. Finally I show some limitations of the FGN models by testing them on the more complex SPEECHCOMMANDS task, against the stronger Carlini-Wagner and Projected Gradient Descent adversarial attacks.

Abstract: Complex systems are characterized by intricate interactions between entities that evolve dynamically over time. Accurate inference of these dynamic relationships is crucial for understanding and predicting system behavior. In this paper, we propose Regulatory Temporal Interaction Network Inference (RiTINI) for inferring time-varying interaction graphs in complex systems using a novel combination of space-and-time graph attentions and graph neural ordinary differential equations (ODEs). RiTINI leverages time-lapse signals on a graph prior, as well as perturbations of signals at various nodes in order to effectively capture the dynamics of the underlying system. This approach is distinct from traditional causal inference networks, which are limited to inferring acyclic and static graphs. In contrast, RiTINI can infer cyclic, directed, and time-varying graphs, providing a more comprehensive and accurate representation of complex systems. The graph attention mechanism in RiTINI allows the model to adaptively focus on the most relevant interactions in time and space, while the graph neural ODEs enable continuous-time modeling of the system's dynamics. We evaluate RiTINI's performance on various simulated and real-world datasets, demonstrating its state-of-the-art capability in inferring interaction graphs compared to previous methods.

Abstract: Offline constrained reinforcement learning (RL) aims to learn a policy that maximizes the expected cumulative reward subject to constraints on expected value of cost functions using an existing dataset. In this paper, we propose Primal-Dual-Critic Algorithm (PDCA), a novel algorithm for offline constrained RL with general function approximation. PDCA runs a primal-dual algorithm on the Lagrangian function estimated by critics. The primal player employs a no-regret policy optimization oracle to maximize the Lagrangian estimate given any choices of the critics and the dual player. The dual player employs a no-regret online linear optimization oracle to minimize the Lagrangian estimate given any choices of the critics and the primal player. We show that PDCA can successfully find a near saddle point of the Lagrangian, which is nearly optimal for the constrained RL problem. Unlike previous work that requires concentrability and strong Bellman completeness assumptions, PDCA only requires concentrability and value function/marginalized importance weight realizability assumptions.

Abstract: The dynamical stability of optimization methods at the vicinity of minima of the loss has recently attracted significant attention. For gradient descent (GD), stable convergence is possible only to minima that are sufficiently flat w.r.t. the step size, and those have been linked with favorable properties of the trained model. However, while the stability threshold of GD is well-known, to date, no explicit expression has been derived for the exact threshold of stochastic GD (SGD). In this paper, we derive such a closed-form expression. Specifically, we provide an explicit condition on the step size $\eta$ that is both necessary and sufficient for the stability of SGD in the mean square sense. Our analysis sheds light on the precise role of the batch size $B$. Particularly, we show that the stability threshold is a monotonically non-decreasing function of the batch size, which means that reducing the batch size can only hurt stability. Furthermore, we show that SGD's stability threshold is equivalent to that of a process which takes in each iteration a full batch gradient step w.p. $1-p$, and a single sample gradient step w.p. $p$, where $p \approx 1/B $. This indicates that even with moderate batch sizes, SGD's stability threshold is very close to that of GD's. Finally, we prove simple necessary conditions for stability, which depend on the batch size, and are easier to compute than the precise threshold. We demonstrate our theoretical findings through experiments on the MNIST dataset.

Abstract: We explore algorithms to select actions in the causal bandit setting where the learner can choose to intervene on a set of random variables related by a causal graph, and the learner sequentially chooses interventions and observes a sample from the interventional distribution. The learner's goal is to quickly find the intervention, among all interventions on observable variables, that maximizes the expectation of an outcome variable. We depart from previous literature by assuming no knowledge of the causal graph except that latent confounders between the outcome and its ancestors are not present. We first show that the unknown graph problem can be exponentially hard in the parents of the outcome. To remedy this, we adopt an additional additive assumption on the outcome which allows us to solve the problem by casting it as an additive combinatorial linear bandit problem with full-bandit feedback. We propose a novel action-elimination algorithm for this setting, show how to apply this algorithm to the causal bandit problem, provide sample complexity bounds, and empirically validate our findings on a suite of randomly generated causal models, effectively showing that one does not need to explicitly learn the parents of the outcome to identify the best intervention.

Abstract: Domain adaptation aims to mitigate distribution shifts among different domains. However, traditional formulations are mostly limited to categorical domains, greatly simplifying nuanced domain relationships in the real world. In this work, we tackle a generalization with taxonomy-structured domains, which formalizes domains with nested, hierarchical similarity structures such as animal species and product catalogs. We build on the classic adversarial framework and introduce a novel taxonomist, which competes with the adversarial discriminator to preserve the taxonomy information. The equilibrium recovers the classic adversarial domain adaptation's solution if given a non-informative domain taxonomy (e.g., a flat taxonomy where all leaf nodes connect to the root node) while yielding non-trivial results with other taxonomies. Empirically, our method achieves state-of-the-art performance on both synthetic and real-world datasets with successful adaptation. Code is available at https://github.com/Wang-ML-Lab/TSDA.

Abstract: Federated Learning (FL) has emerged as a promising approach for collaborative model training without sharing private data. However, privacy concerns regarding information exchanged during FL have received significant research attention. Gradient Inversion Attacks (GIAs) have been proposed to reconstruct the private data retained by local clients from the exchanged gradients. While recovering private data, the data dimensions and the model complexity increase, which thwart data reconstruction by GIAs. Existing methods adopt prior knowledge about private data to overcome those challenges. In this paper, we first observe that GIAs with gradients from a single iteration fail to reconstruct private data due to insufficient dimensions of leaked gradients, complex model architectures, and invalid gradient information. We investigate a Temporal Gradient Inversion Attack with a Robust Optimization framework, called TGIAs-RO, which recovers private data without any prior knowledge by leveraging multiple temporal gradients. To eliminate the negative impacts of outliers, e.g., invalid gradients for collaborative optimization, robust statistics are proposed. Theoretical guarantees on the recovery performance and robustness of TGIAs-RO against invalid gradients are also provided. Extensive empirical results on MNIST, CIFAR10, ImageNet and Reuters 21578 datasets show that the proposed TGIAs-RO with 10 temporal gradients improves reconstruction performance compared to state-of-the-art methods, even for large batch sizes (up to 128), complex models like ResNet18, and large datasets like ImageNet (224*224 pixels). Furthermore, the proposed attack method inspires further exploration of privacy-preserving methods in the context of FL.

Abstract: We study the problem of learning a single neuron with respect to the $L_2^2$-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal $L_2^2$-error within a constant factor. Our algorithm applies under much milder distributional assumptions compared to prior work. The key ingredient enabling our results is a novel connection to local error bounds from optimization theory.

Abstract: In this paper, we investigate the streaming bandits problem, wherein the learner aims to minimize regret by dealing with online arriving arms and sublinear arm memory. We establish the tight worst-case regret lower bound of $\Omega \left( (TB)^{\alpha} K^{1-\alpha}\right), \alpha = 2^{B} / (2^{B+1}-1)$ for any algorithm with a time horizon $T$, number of arms $K$, and number of passes $B$. The result reveals a separation between the stochastic bandits problem in the classical centralized setting and the streaming setting with bounded arm memory. Notably, in comparison to the well-known $\Omega(\sqrt{KT})$ lower bound, an additional double logarithmic factor is unavoidable for any streaming bandits algorithm with sublinear memory permitted. Furthermore, we establish the first instance-dependent lower bound of $\Omega \left(T^{1/(B+1)} \sum_{\Delta_x>0} \frac{\mu^*}{\Delta_x}\right)$ for streaming bandits. These lower bounds are derived through a unique reduction from the regret-minimization setting to the sample complexity analysis for a sequence of $\epsilon$-optimal arms identification tasks, which maybe of independent interest. To complement the lower bound, we also provide a multi-pass algorithm that achieves a regret upper bound of $\tilde{O} \left( (TB)^{\alpha} K^{1 - \alpha}\right)$ using constant arm memory.

Abstract: Stochastic min-max optimization has gained interest in the machine learning community with the advancements in GANs and adversarial training. Although game optimization is fairly well understood in the deterministic setting, some issues persist in the stochastic regime. Recent work has shown that stochastic gradient descent-ascent methods such as the optimistic gradient are highly sensitive to noise or can fail to converge. Although alternative strategies exist, they can be prohibitively expensive. We introduce Omega, a method with optimistic-like updates that mitigates the impact of noise by incorporating an EMA of historic gradients in its update rule. We also explore a variation of this algorithm that incorporates momentum. Although we do not provide convergence guarantees, our experiments on stochastic games show that Omega outperforms the optimistic gradient method when applied to linear players.

Abstract: Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be highly challenging, especially when observed variables are generated by causally related latent variables and the relationships are nonlinear. In this work, we investigate the identification problem for nonlinear latent hierarchical causal models in which observed variables are generated by a set of causally related latent variables, and some latent variables may not have observed children. We show that the identifiability of both causal structure and latent variables can be achieved under mild assumptions: on causal structures, we allow for the existence of multiple paths between any pair of variables in the graph, which relaxes latent tree assumptions in prior work; on structural functions, we do not make parametric assumptions, thus permitting general nonlinearity and multi-dimensional continuous variables. Specifically, we first develop a basic identification criterion in the form of novel identifiability guarantees for an elementary latent variable model. Leveraging this criterion, we show that both causal structures and latent variables of the hierarchical model can be identified asymptotically by explicitly constructing an estimation procedure. To the best of our knowledge, our work is the first to establish identifiability guarantees for both causal structures and latent variables in nonlinear latent hierarchical models.

Abstract: Causal mediation analysis (CMA) is a powerful method to dissect the total effect of a treatment into direct and mediated effects within the potential outcome framework. This is important in many scientific applications to identify the underlying mechanisms of a treatment effect. However, in many scientific applications the mediator is unobserved, but there may exist related measurements. For example, we may want to identify how changes in brain activity or structure mediate an antidepressant's effect on behavior, but we may only have access to electrophysiological or imaging brain measurements. To date, most CMA methods assume that the mediator is one-dimensional and observable, which oversimplifies such real-world scenarios. To overcome this limitation, we introduce a CMA framework that can handle complex and indirectly observed mediators based on the identifiable variational autoencoder (iVAE) architecture. We prove that the true joint distribution over observed and latent variables is identifiable with the proposed method. Additionally, our framework captures a disentangled representation of the indirectly observed mediator and yields accurate estimation of the direct and mediated effects in synthetic and semi-synthetic experiments, providing evidence of its potential utility in real-world applications.

Abstract: Imitation learning has achieved great success in many sequential decision-making tasks, in which a neural agent is learned by imitating collected human demonstrations. However, existing algorithms typically require a large number of high-quality demonstrations that are difficult and expensive to collect. Usually, a trade-off needs to be made between demonstration quality and quantity in practice. Targeting this problem, in this work we consider the imitation of sub-optimal demonstrations, with both a small clean demonstration set and a large noisy set. Some pioneering works have been proposed, but they suffer from many limitations, e.g., assuming a demonstration to be of the same optimality throughout time steps and failing to provide any interpretation w.r.t knowledge learned from the noisy set. Addressing these problems, we propose {\method} by evaluating and imitating at the sub-demonstration level, encoding action primitives of varying quality into different skills. Concretely, {\method} consists of a high-level controller to discover skills and a skill-conditioned module to capture action-taking policies, and is trained following a two-phase pipeline by first discovering skills with all demonstrations and then adapting the controller to only the clean set. A mutual-information-based regularization and a dynamic sub-demonstration optimality estimator are designed to promote disentanglement in the skill space. Extensive experiments are conducted over two gym environments and a real-world healthcare dataset to demonstrate the superiority of {\method} in learning from sub-optimal demonstrations and its improved interpretability by examining learned skills.

Abstract: We consider policy optimization in contextual bandits, where one is given a fixed dataset of logged interactions. While pessimistic regularizers are typically used to mitigate distribution shift, prior implementations thereof are not computationally efficient. We present the first oracle-efficient algorithm for pessimistic policy optimization: it reduces to supervised learning, leading to broad applicability. We also obtain best-effort statistical guarantees analogous to those for pessimistic approaches in prior work. We instantiate our approach for both discrete and continuous actions. We perform extensive experiments in both settings, showing advantage over unregularized policy optimization across a wide range of configurations.

Abstract: In several practical applications of federated learning (FL), the clients are highly heterogeneous in terms of both their data and compute resources, and therefore enforcing the same model architecture for each client is very limiting. Moreover, the need for uncertainty quantification and data privacy constraints are often particularly amplified for clients that have limited local data. This paper presents a unified FL framework to simultaneously address all these constraints and concerns, based on training customized local Bayesian models that learn well even in the absence of large local datasets. A Bayesian framework provides a natural way of incorporating supervision in the form of prior distributions. We use priors in the functional (output) space of the networks to facilitate collaboration across heterogeneous clients. Moreover, formal differential privacy guarantees are provided for this framework. Experiments on standard FL datasets demonstrate that our approach outperforms strong baselines in both homogeneous and heterogeneous settings and under strict privacy constraints, while also providing characterizations of model uncertainties.

Abstract: Supervised contrastive loss (SCL) is a competitive and often superior alternative to the cross-entropy (CE) loss for classification. In this paper we ask: what differences in the learning process occur when the two different loss functions are being optimized? To answer this question, our main finding is that the geometry of embeddings learned by SCL forms an orthogonal frame (OF) regardless of the number of training examples per class. This is in contrast to the CE loss, for which previous work has shown that it learns embeddings geometries that are highly dependent on the class sizes. We arrive at our finding theoretically, by proving that the global minimizers of an unconstrained features model with SCL loss and entry-wise non-negativity constraints form an OF. We then validate the model's prediction by conducting experiments with standard deep-learning models on benchmark vision datasets. Finally, our analysis and experiments reveal that the batching scheme chosen during SCL training plays a critical role in determining the quality of convergence to the OF geometry. This finding motivates a simple algorithm wherein the addition of a few binding examples in each batch significantly speeds up the occurrence of the OF geometry.

Abstract: We present Generalized LoRA (GLoRA), an advanced approach for universal parameter-efficient fine-tuning tasks. Enhancing Low-Rank Adaptation (LoRA), GLoRA employs a generalized prompt module to optimize pre-trained model weights and adjust intermediate activations, providing more flexibility and capability across diverse tasks and datasets. Moreover, GLoRA facilitates efficient parameter adaptation by employing a scalable, modular, layer-wise structure search that learns individual adapter of each layer. Originating from a unified mathematical formulation, GLoRA exhibits strong transfer learning, few-shot learning and domain generalization abilities, as it adjusts to new tasks through additional dimensions on weights and activations. Comprehensive experiments demonstrate that GLoRA outperforms all previous methods in natural, specialized, and structured benchmarks, achieving superior accuracy with fewer parameters and computations on various datasets. Furthermore, our structural re-parameterization design ensures that GLoRA incurs no extra inference cost, rendering it a practical solution for resource-limited applications. Code is available at: https://github.com/Arnav0400/ViT-Slim/tree/master/GLoRA.