In off-policy policy evaluation (OPE) tasks within reinforcement learning, Temporal Difference Learning(TD) and Fitted Q-Iteration (FQI) have traditionally been viewed as differing in the number of updates toward the target value function: TD makes one update, FQI makes an infinite number, and Partial Fitted Q-Iteration (PFQI) performs a finite number. We show that this view is not accurate, and provide a new mathematical perspective under linear value function approximation that unifies these methods as a single iterative method solving the same linear system, but using different matrix splitting schemes and preconditioners. We show that increasing the number of updates under the same target value function, i.e., the target network technique, is a transition from using a constant preconditioner to using a data-feature adaptive preconditioner. This elucidates, for the first time, why TD convergence does not necessarily imply FQI convergence, and establishes tight convergence connections among TD, PFQI, and FQI. Our framework enables sharper theoretical results than previous work and characterization of the convergence conditions for each algorithm, without relying on assumptions about the features (e.g., linear independence). We also provide an encoder-decoder perspective to better understand the convergence conditions of TD, and prove, for the first time, that when a large learning rate doesn't work, trying a smaller one may help. Our framework also leads to the discovery of new crucial conditions on features for convergence, and shows how common assumptions about features influence convergence, e.g., the assumption of linearly independent features can be dropped without compromising the convergence guarantees of stochastic TD in the on-policy setting. This paper is also the first to introduce matrix splitting into the convergence analysis of these algorithms.

In constrained MDPs (CMDPs) with adversarial rewards and constraints, a known impossibility result prevents any algorithm from attaining sublinear regret and constraint violation, when competing against a best-in-hindsight policy that satisfies the constraints on average. In this paper, we show how to ease such a negative result, by considering settings that generalize both stochastic CMDPs and adversarial ones. We provide algorithms whose performances smoothly degrade as the level of environment adverseness increases. Specifically, they attain eO( T +C) regret and positive constraint violation under bandit feedback, where C measures the adverseness of rewards and constraints. This is C = Θ(T) in the worst case, coherently with the impossibility result for adversarial CMDPs. First, we design an algorithm with the desired guarantees when C is known. Then, in the case C is unknown, we obtain the same results by embedding multiple instances of such an algorithm in a general meta-procedure, which suitably selects them so as to balance the trade-off between regret and constraint violation.

We propose and analyze a model-based bootstrap for transition kernels in finite controlled Markov chains (CMCs) with possibly nonstationary or history-dependent control policies, a setting that arises naturally in offline reinforcement learning (RL) when the behavior policy generating the data is unknown. We establish distributional consistency of the bootstrap transition estimator in both a single long-chain regime and the episodic offline RL regime. The key technical tools are a novel bootstrap law of large numbers (LLN) for the visitation counts and a novel use of the martingale central limit theorem (CLT) for the bootstrap transition increments. We extend bootstrap distributional consistency to the downstream targets of offline policy evaluation (OPE) and optimal policy recovery (OPR) via the delta method by verifying Hadamard differentiability of the Bellman operators, yielding asymptotically valid confidence intervals for value and $Q$-functions. Experiments on the RiverSwim problem show that the proposed bootstrap confidence intervals (CIs), especially the percentile CIs, outperform the episodic bootstrap and plug-in CLT CIs, and are often close to nominal ($50\%$, $90\%$, $95\%$) coverage, while the baselines are poorly calibrated at small sample sizes and short episode lengths.

Neural Information Processing Systems http://nips.cc/

Offline policy learning is aimed at learning decision-making policies using existing datasets of trajectories without collecting additional data. The primary motivation for using reinforcement learning (RL) instead of supervised learning techniques such as behavior cloning is to find a policy that achieves a higher average return than the trajectories constituting the dataset. However, we empirically find that when a dataset is dominated by suboptimal trajectories, state-of-the-art offline RL algorithms do not substantially improve over the average return of trajectories in the dataset. We argue this is due to an assumption made by current offline RL algorithms of staying close to the trajectories in the dataset. If the dataset primarily consists of sub-optimal trajectories, this assumption forces the policy to mimic the suboptimal actions. We overcome this issue by proposing a sampling strategy that enables the policy to only be constrained to "good data" rather than all actions in the dataset (i.e., uniform sampling). We present a realization of the sampling strategy and an algorithm that can be used as a plug-and-play module in standard offline RL algorithms. Our evaluation demonstrates significant performance gains in 72 imbalanced datasets, D4RL dataset, and across three different offline RL algorithms.