The cooperative Multi-Agent Reinforcement Learning (MARL) with permutation invariant agents framework has achieved tremendous empirical successes in real-world applications. Unfortunately, the theoretical understanding of this MARL problem is lacking due to the curse of many agents and the limited exploration of the relational reasoning in existing works. In this paper, we verify that the transformer implements complex relational reasoning, and we propose and analyze model-free and model-based offline MARL algorithms with the transformer approximators. We prove that the suboptimality gaps of the model-free and model-based algorithms are independent of and logarithmic in the number of agents respectively, which mitigates the curse of many agents. These results are consequences of a novel generalization error bound of the transformer and a novel analysis of the Maximum Likelihood Estimate (MLE) of the system dynamics with the transformer. Our model-based algorithm is the first provably efficient MARL algorithm that explicitly exploits the permutation invariance of the agents. Our improved generalization bound may be of independent interest and is applicable to other regression problems related to the transformer beyond MARL.

We present the problem of reinforcement learning with exogenous termination. We define the Termination Markov Decision Process (TerMDP), an extension of the MDP framework, in which episodes may be interrupted by an external non-Markovian observer.

Temporal Difference (TD) learning is ubiquitous in reinforcement learning, where it is often combined with off-policy sampling and function approximation. Unfortunately learning with this combination (known as the deadly triad), exhibits instability and unbounded error. To account for this, modern Reinforcement Learning methods often implicitly (or sometimes explicitly) assume that regularization is sufficient to mitigate the problem in practice; indeed, the standard deadly triad examples from the literature can be ``fixed'' via proper regularization. In this paper, we introduce a series of new counterexamples to show that the instability and unbounded error of TD methods is not solved by regularization. We demonstrate that, in the off-policy setting with linear function approximation, TD methods can fail to learn a non-trivial value function under any amount of regularization; we further show that regularization can induce divergence under common conditions; and we show that one of the most promising methods to mitigate this divergence (Emphatic TD algorithms) may also diverge under regularization. We further demonstrate such divergence when using neural networks as function approximators. Thus, we argue that the role of regularization in TD methods needs to be reconsidered, given that it is insufficient to prevent divergence and may itself introduce instability. There needs to be much more care in the practical and theoretical application of regularization to Reinforcement Learning methods.

In reinforcement learning (RL), it is easier to solve a task if given a good representation. While deep RL should automatically acquire such good representations, prior work often finds that learning representations in an end-to-end fashion is unstable and instead equip RL algorithms with additional representation learning parts (e.g., auxiliary losses, data augmentation). How can we design RL algorithms that directly acquire good representations? In this paper, instead of adding representation learning parts to an existing RL algorithm, we show (contrastive) representation learning methods are already RL algorithms in their own right. To do this, we build upon prior work and apply contrastive representation learning to action-labeled trajectories, in such a way that the (inner product of) learned representations exactly corresponds to a goal-conditioned value function. We use this idea to reinterpret a prior RL method as performing contrastive learning, and then use the idea to propose a much simpler method that achieves similar performance. Across a range of goal-conditioned RL tasks, we demonstrate that contrastive RL methods achieve higher success rates than prior non-contrastive methods.

Recursion is the fundamental paradigm to finitely describe potentially infinite objects. As state-of-the-art reinforcement learning (RL) algorithms cannot directly reason about recursion, they must rely on the practitioner's ingenuity in designing a suitable flat representation of the environment. The resulting manual feature constructions and approximations are cumbersome and error-prone; their lack of transparency hampers scalability. To overcome these challenges, we develop RL algorithms capable of computing optimal policies in environments described as a collection of Markov decision processes (MDPs) that can recursively invoke one another. Each constituent MDP is characterized by several entry and exit points that correspond to input and output values of these invocations. These recursive MDPs (or RMDPs) are expressively equivalent to probabilistic pushdown systems (with call-stack playing the role of the pushdown stack), and can model probabilistic programs with recursive procedural calls. We introduce Recursive Q-learning---a model-free RL algorithm for RMDPs---and prove that it converges for finite, single-exit and deterministic multi-exit RMDPs under mild assumptions.

A central problem in online learning and decision making---from bandits to reinforcement learning---is to understand what modeling assumptions lead to sample-efficient learning guarantees. We consider a general adversarial decision making framework that encompasses (structured) bandit problems with adversarial rewards and reinforcement learning problems with adversarial dynamics. Our main result is to show---via new upper and lower bounds---that the Decision-Estimation Coefficient, a complexity measure introduced by Foster et al. in the stochastic counterpart to our setting, is necessary and sufficient to obtain low regret for adversarial decision making. However, compared to the stochastic setting, one must apply the Decision-Estimation Coefficient to the convex hull of the class of models (or, hypotheses) under consideration. This establishes that the price of accommodating adversarial rewards or dynamics is governed by the behavior of the model class under convexification, and recovers a number of existing results --both positive and negative. En route to obtaining these guarantees, we provide new structural results that connect the Decision-Estimation Coefficient to variants of other well-known complexity measures, including the Information Ratio of Russo and Van Roy and the Exploration-by-Optimization objective of Lattimore and György.

Gradient-based methods for optimisation of objectives in stochastic settings with unknown or intractable dynamics require estimators of derivatives. We derive an objective that, under automatic differentiation, produces low-variance unbiased estimators of derivatives at any order. Our objective is compatible with arbitrary advantage estimators, which allows the control of the bias and variance of any-order derivatives when using function approximation. Furthermore, we propose a method to trade off bias and variance of higher order derivatives by discounting the impact of more distant causal dependencies. We demonstrate the correctness and utility of our estimator in analytically tractable MDPs and in meta-reinforcement-learning for continuous control.

We propose a model-based reinforcement learning framework to derive untargeted poisoning attacks against federated learning (FL) systems. Our framework first approximates the distribution of the clients' aggregated data using model updates from the server. The learned distribution is then used to build a simulator of the FL environment, which is utilized to learn an adaptive attack policy through reinforcement learning. Our framework is capable of learning strong attacks automatically even when the server adopts a robust aggregation rule. We further derive an upper bound on the attacker's performance loss due to inaccurate distribution estimation. Experimental results on real-world datasets demonstrate that the proposed attack framework significantly outperforms state-of-the-art poisoning attacks. This indicates the importance of developing adaptive defenses for FL systems.

Safe exploration is essential for the practical use of reinforcement learning (RL) in many real-world scenarios. In this paper, we present a generalized safe exploration (GSE) problem as a unified formulation of common safe exploration problems. We then propose a solution of the GSE problem in the form of a meta-algorithm for safe exploration, MASE, which combines an unconstrained RL algorithm with an uncertainty quantifier to guarantee safety in the current episode while properly penalizing unsafe explorations before actual safety violation to discourage them in future episodes. The advantage of MASE is that we can optimize a policy while guaranteeing with a high probability that no safety constraint will be violated under proper assumptions. Specifically, we present two variants of MASE with different constructions of the uncertainty quantifier: one based on generalized linear models with theoretical guarantees of safety and near-optimality, and another that combines a Gaussian process to ensure safety with a deep RL algorithm to maximize the reward. Finally, we demonstrate that our proposed algorithm achieves better performance than state-of-the-art algorithms on grid-world and Safety Gym benchmarks without violating any safety constraints, even during training.

Our work focuses on training RL agents on multiple visually diverse environments to improve observational generalization performance. In prior methods, policy and value networks are separately optimized using a disjoint network architecture to avoid interference and obtain a more accurate value function. We identify that a value network in the multi-environment setting is more challenging to optimize and prone to memorizing the training data than in the conventional single-environment setting. In addition, we find that appropriate regularization on the value network is necessary to improve both training and test performance. To this end, we propose Delayed-Critic Policy Gradient (DCPG), a policy gradient algorithm that implicitly penalizes value estimates by optimizing the value network less frequently with more training data than the policy network. This can be implemented using a single unified network architecture. Furthermore, we introduce a simple self-supervised task that learns the forward and inverse dynamics of environments using a single discriminator, which can be jointly optimized with the value network. Our proposed algorithms significantly improve observational generalization performance and sample efficiency on the Procgen Benchmark.