Inthiswork,weconsider thescenario where agent limitations may entirely preclude identifying an exactly value-equivalent model, immediately giving rise to a trade-off between identifying a model that is simple enough to learn while only incurring bounded sub-optimality.

We study model-free reinforcement learning (RL) in non-stationary finite-horizon episodic Markov decision processes (MDPs) without prior knowledge of the non-stationarity. We focus on the piecewise-stationary (PS) setting, where both the reward and transition dynamics can change an arbitrary number of times. We propose Detection Augmented Reinforcement Learning (DARLING), a modular wrapper for PS-RL that applies to both tabular and linear MDPs, without knowledge of the changes. Under certain change-point separation and reachability conditions, DARLING improves the best available dynamic regret bounds in both settings and yields strong empirical performance. We further establish the first minimax lower bounds for PS-RL in tabular and linear MDPs, showing that DARLING is the first nearly optimal algorithm. Experiments on standard benchmarks demonstrate that DARLING consistently surpasses the state-of-the-art methods across diverse non-stationary scenarios.

We study offline-online reinforcement learning in linear mixture Markov decision processes (MDPs) under environment shift. In the offline phase, data are collected by an unknown behavior policy and may come from a mismatched environment, while in the online phase the learner interacts with the target environment. We propose an algorithm that adaptively leverages offline data. When the offline data are informative, either due to sufficient coverage or small environment shift, the algorithm provably improves over purely online learning. When the offline data are uninformative, it safely ignores them and matches the online-only performance. We establish regret upper bounds that explicitly characterize when offline data are beneficial, together with nearly matching lower bounds. Numerical experiments further corroborate our theoretical findings.

Online reinforcement learning in infinite-horizon Markov decision processes (MDPs) remains less theoretically and algorithmically developed than its episodic counterpart, with many algorithms suffering from high ``burn-in'' costs and failing to adapt to benign instance-specific complexity. In this work, we address these shortcomings for two infinite-horizon objectives: the classical average-reward regret and the $γ$-regret. We develop a single tractable UCB-style algorithm applicable to both settings, which achieves the first optimal variance-dependent regret guarantees. Our regret bounds in both settings take the form $\tilde{O}( \sqrt{SA\,\text{Var}} + \text{lower-order terms})$, where $S,A$ are the state and action space sizes, and $\text{Var}$ captures cumulative transition variance. This implies minimax-optimal average-reward and $γ$-regret bounds in the worst case but also adapts to easier problem instances, for example yielding nearly constant regret in deterministic MDPs. Furthermore, our algorithm enjoys significantly improved lower-order terms for the average-reward setting. With prior knowledge of the optimal bias span $\Vert h^\star\Vert_\text{sp}$, our algorithm obtains lower-order terms scaling as $\Vert h^\star\Vert_\text{sp} S^2 A$, which we prove is optimal in both $\Vert h^\star\Vert_\text{sp}$ and $A$. Without prior knowledge, we prove that no algorithm can have lower-order terms smaller than $\Vert h^\star \Vert_\text{sp}^2 S A$, and we provide a prior-free algorithm whose lower-order terms scale as $\Vert h^\star\Vert_\text{sp}^2 S^3 A$, nearly matching this lower bound. Taken together, these results completely characterize the optimal dependence on $\Vert h^\star\Vert_\text{sp}$ in both leading and lower-order terms, and reveal a fundamental gap in what is achievable with and without prior knowledge.

This paper proposes REFUEL, a reinforcement learning method with two techniques: reward shapingand feature rebuilding, to improve the performance of online symptom checking for disease diagnosis.

We consider the problem of learning an unknown Markov Decision Process (MDP) that is weakly communicating in the infinite horizon setting. We propose a Thompson Sampling-based reinforcement learning algorithm with dynamic episodes (TSDE). At the beginning of each episode, the algorithm generates a sample from the posterior distribution over the unknown model parameters. It then follows the optimal stationary policy for the sampled model for the rest of the episode. The duration of each episode is dynamically determined by two stopping criteria.

Count-based exploration algorithms are known to perform near-optimally when used in conjunction with tabular reinforcement learning (RL) methods for solving small discrete Markov decision processes (MDPs). It is generally thought that count-based methods cannot be applied in high-dimensional state spaces, since most states will only occur once. Recent deep RL exploration strategies are able to deal with high-dimensional continuous state spaces through complex heuristics, often relying on optimism in the face of uncertainty or intrinsic motivation. In this work, we describe a surprising finding: a simple generalization of the classic count-based approach can reach near state-of-the-art performance on various high-dimensional and/or continuous deep RL benchmarks. States are mapped to hash codes, which allows to count their occurrences with a hash table.

In classical reinforcement learning agents accept arbitrary short term loss for long term gain when exploring their environment. This is infeasible for safety critical applications such as robotics, where even a single unsafe action may cause system failure or harm the environment. In this paper, we address the problem of safely exploring finite Markov decision processes (MDP). We define safety in terms of an a priori unknown safety constraint that depends on states and actions and satisfies certain regularity conditions expressed via a Gaussian process prior. We develop a novel algorithm, SAFEMDP, for this task and prove that it completely explores the safely reachable part of the MDP without violating the safety constraint. To achieve this, it cautiously explores safe states and actions in order to gain statistical confidence about the safety of unvisited state-action pairs from noisy observations collected while navigating the environment. Moreover, the algorithm explicitly considers reachability when exploring the MDP, ensuring that it does not get stuck in any state with no safe way out. We demonstrate our method on digital terrain models for the task of exploring an unknown map with a rover.

We study the sampling-based planning problem in Markov decision processes (MDPs) that we can access only through a generative model, usually referred to as Monte-Carlo planning. Our objective is to return a good estimate of the optimal value function at any state while minimizing the number of calls to the generative model, i.e. the sample complexity. We propose a new algorithm, TrailBlazer, able to handle MDPs with a finite or an infinite number of transitions from state-action to next states. TrailBlazer is an adaptive algorithm that exploits possible structures of the MDP by exploring only a subset of states reachable by following near-optimal policies. We provide bounds on its sample complexity that depend on a measure of the quantity of near-optimal states. The algorithm behavior can be considered as an extension of Monte-Carlo sampling (for estimating an expectation) to problems that alternate maximization (over actions) and expectation (over next states). Finally, another appealing feature of TrailBlazer is that it is simple to implement and computationally efficient.

While designing the state space of an MDP, it is common to include states that are transient or not reachable by any policy (e.g., in mountain car, the product space of speed and position contains configurations that are not physically reachable).