Episodic RL

We study regret minimization for time-homogeneous episodic tabular reinforcement learning with $S$ states and $A$ actions under non-interactive $ε$-local differential privacy (LDP). In each episode $k \in [K]$, the decision-maker sends a policy to a user, the user executes the policy for $H$ steps, and sends an $ε$-locally differentially private message back to the decision-maker. When $H=1$, the problem reduces to an LDP contextual bandit with $S$ contexts, $A$ arms and horizon $K$. We prove that the minimax regret is $\min\bigg(K, \frac{ \sqrt{\max( S, \exp(ε) + 1) S A K (\exp(ε) + 1)}}{\exp(ε) - 1}\bigg)$, up to constants and a $\sqrt{\log(A)}$ factor. The upper bound is achieved by an adaptation of EXP3 and a unary encoding mechanism. When $H > 1$, and for small $ε$, we show a lower bound in $Ω(HS\frac{\sqrt{A K}}ε)$ and an upper bound in $\tilde{O}(H^2 S^2 \frac{\sqrt{ AK}}ε)$. The upper bound is achieved by an algorithm based on UCBVI and a unary encoding mechanism. For small $ε$, these bounds improve the previously known lower bound by a factor $\sqrt{S}$ and the previously known upper bound by a factor of $H \sqrt{A}$.

In this paper, we study the regret minimization problem in episodic tabular MDPs. Our algorithm achieves the first expected regret bound scaling as $\sqrt{H^3 S A K}$ for sufficiently large $K$, where $H$ is the episode length, $K$ is the number of episodes, and $S$ and $A$ are the numbers of states and actions, respectively. Our method is the first to match the minimax lower bound without extra polylog factors. We introduce a variant of UCBVI which does not maintain strictly optimistic estimates, and uses MOSS-style exploration bonuses whose logarithmic terms adapt to both visit counts and estimated variances. A key challenge is controlling the propagation of errors caused by under-optimism, which we accomplish in an occupancy-weighted way, avoiding logarithmic overhead that would be incurred by uniform-over-rows concentration. Our analysis develops time-uniform and variance-aware concentration bounds that may be of independent interest. As a corollary we also develop an algorithm for $(\varepsilon, δ)$-PAC best-policy identification, which is the first to match the $Ω\big(H^3 SA\log(\frac{1}δ)\varepsilon^{-2}\big)$ minimax lower bound up to constants in some regimes.

Many real-world reinforcement learning (RL) problems evolve in continuous time, where decisions occur at irregular, event-driven intervals rather than at fixed discrete steps. We study episodic continuous-time Markov Decision Processes (MDPs) in which decision epochs are governed by a homogeneous Poisson process and the reward and transition dynamics vary smoothly over time. We consider both a fixed number of jumps per episode and a fixed time budget with a random number of Poisson decision epochs. Under a Lipschitz continuity assumption in time, we exploit local smoothness through discretization and extend both UCRL (Auer and Ortner 2006) and Q-learning (Jin et al. 2018) to this setting, proving $\widetilde{O}(T^{2/3})$ regret bounds for both model-based and model-free algorithms. Finally, we establish matching $\widetildeΩ(T^{2/3})$ minimax lower bounds, showing that the rate is optimal up to logarithmic factors. These results provide the first tight regret guarantees for Lipschitz-smooth continuous-time episodic MDPs with Poisson decision epochs.

We study decentralized multi-player reinforcement learning in episodic tabular Markov decision processes (MDPs) under three forms of information asymmetry: (A) unobserved actions with common rewards, (B) observed actions with independent rewards, and (C) unobserved actions with independent rewards. Players cannot communicate during learning but may agree on a protocol a priori. For Problems A and B we propose mQ-learning and mQ-learning-intervals, achieving $\tilde{O}(\sqrt{H^4 S A_{\text{joint}}\, T})$ regret, where $H$ is the horizon, $S$ the state count, $T = KH$ the total steps, and $A_{\text{joint}} = \prod_{i=1}^M |\mathcal{A}_i|$ the joint action space across $M$ players. For Problem C we give mEXC and mEXC-Bellman, two-phase explore-then-commit algorithms with regret $\tilde{O}(H (S A_{\text{joint}})^{1/3} T^{2/3})$. Against the centralized joint-action benchmark, decentralized learning under information asymmetry matches the single-agent Q-learning rate of \cite{jin2018q} up to logarithmic factors. Because $A_{\text{joint}}$ grows exponentially in $M$, the bounds are most meaningful for small $M$ or small per-player action sets.

Cooperative Multi-Agent Reinforcement Learning (MARL) frequently suffers from severe reward sparsity and exploration bottlenecks. While episodic memory mechanisms mitigate these issues by reusing high-return trajectories, they often trap agents in local optima due to unconstrained incentive distribution and semantic representation collapse. To address this, we propose Episodic Memory Temporal Consistency (EMTC), a framework that robustly constructs and selectively leverages historical experiences. EMTC introduces two synergistic components: (1) a Temporally Consistent Semantic Embedder that integrates contrastive learning with time-conditioned state reconstruction, preventing representation collapse and enabling precise memory retrieval; and (2) a Temporal Consistency Gating Mechanism that dynamically modulates episodic incentives based on temporal consistency error. This adaptive gate filters misleading signals from pseudo-successful trajectories, effectively mitigating Q-value overestimation. We provide theoretical guarantees, establishing a strict error bound that directly links the observable temporal consistency error to the underlying trajectory optimality and representation quality. Extensive evaluations on the SMAC and GRF benchmarks demonstrate that EMTC consistently outperforms state-of-the-art baselines. Notably, compared to the strongest episodic baseline, EMTC achieves absolute win-rate improvements of up to 24% in super-hard SMAC scenarios and an average improvement of 28% across GRF tasks.

Pure exploration in episodic Reinforcement Learning has primarily focused on Best Policy Identification (BPI), which seeks to identify a (near)-optimal policy with high confidence. Motivated by practical settings where a ``good enough'' policy suffices, we study an alternate objective of Good Policy Identification (GPI). For a given reward threshold $μ_0$, GPI only requires identifying a policy with expected reward in an episode at least $μ_0$ if such a policy exists (positive instance), or declaring None if no such policy exists (negative instance). We formalize GPI under the fixed-confidence setting. We require the output to be correct with probability $\geq 1-δ$, and seek to minimize the expected sample complexity, which is the expected number of episodes explored for the output. We propose a novel algorithm BEE-GPI, and derive theoretically-grounded upper bounds on its sample complexity for positive and negative instances. Notably, for positive instances, the coefficient of $\log 1/δ$ in our upper bound is $O(H^2/(V^* - μ_0)^2)$, where $H$ is the episode length and $V^*$ is the optimal expected reward in an episode. The coefficient does not depend on the action and state space sizes otherwise, in sharp contrast to the sample complexity in BPI. We further establish lower bound results to show the near-optimality of BEE-GPI and the necessity of the $1/(V^* -μ)^2$ term. Numerical experiments further validate the efficiency of our approach.

Exploration is a prerequisite for learning useful behaviors in sparse-reward, long-horizon tasks, particularly within 3D environments. Curiosity-driven reinforcement learning addresses this via intrinsic rewards derived from the mismatch between the agent's predictive model of the world and reality. However, translating this intrinsic motivation to complex, photorealistic environments remains difficult, as agents can become trapped in local loops and receive fresh rewards for revisiting forgotten states. In this work, we demonstrate that this failure stems from a lack of spatial persistence and episodic context. We show that effective curiosity requires a model of the world that is persistent and continuously updated, paired with an agent that maintains an episodic trajectory history to navigate toward novel regions. We achieve this using an online 3D reconstruction as a persistent model of the world, while the agent policy is parameterized as a sequence model over RGB observations to maintain episodic context. This design enables effective exploration during training while allowing the agent to navigate using solely RGB frames at deployment. Trained purely via curiosity on HM3D, our agent outperforms RL-based active mapping baselines and generalizes zero-shot to Gibson and AI-generated worlds. Our end-to-end policy enables efficient adaptation to downstream tasks, such as apple picking and image-goal navigation, outperforming from-scratch baselines. Please see video results at https://recuriosity.github.io/.

We study model-free Q-learning in finite-horizon episodic Markov Decision Processes (MDPs) with stationary dynamics across episodes. We identify a central issue in nascent model-free posterior-sampling works: the reliance on delayed learning in order to prove theoretical guarantees. In particular, we identify three opportunities for faster learning - (i) value-function update order, (ii) update frequencies, and (iii) value-function initialization. Using Wang et al.'s RandomizedQ as a basis, we illustrate these changes and their individual (as well as cumulative) impact in multiple empirical studies. We find that our combined modifications, termed ReversedQ, improve scaled mean cumulative reward compared to RandomizedQ, from 9.53% to 78.78% in the Bidirectional Diabolical Combination Lock (BDCL), and from 21.76% to 61.81% in a chain MDP.

We study episodic reinforcement learning with fixed reward and transition functions, but with episode-dependent admissible action sets that are observed at the start of each episode. Performance is measured by cumulative regret against the episode-wise optimal value, $\sum_{k=1}^K [V^{*,M^k} - V^{π^k,M^k}]$, where $M^k$ represents the action context in the $k$-th episode. We show that the MVP algorithm naturally extends to this framework and enjoys strong theoretical guarantees. In particular, we establish a minimax regret bound of $\widetilde{O}(\sqrt{SAH^3K\log L})$ for adversarial contexts, where $L$ denotes the number of possible contexts. This result implies a regret bound of $\widetilde{O}(\sqrt{SAH^3K})$ for stochastic contexts. We further translate the stochastic regret guarantee into a sample complexity bound of $\widetilde{O}(SAH^3/ε^2)$ for a fixed context distribution. In addition, we derive a gap-dependent regret bound of $$\widetilde O\left( \inf_{p\in [0,1)} \left( \frac{1}{Δ_{\min}^{p}} + pKΔ_{\min}^{p} \right)\log K \cdot \mathrm{poly}(S,A,H) \right),$$ where $Δ_{\min}^{p}$ is the global $p$-trimmed positive-gap floor over suboptimal $(h,s,a)$ triples. This bound can substantially improve upon the minimax rate when the relevant suboptimality gaps are large.

Differential temporal difference (TD) methods are value-based reinforcement learning algorithms that have been proposed for infinite-horizon problems. They rely on reward centering, where each reward is centered by the average reward. This keeps the return bounded and removes a value function's state-independent offset. However, reward centering can alter the optimal policy in episodic problems, limiting its applicability. Motivated by recent works that emphasize the role of normalization in streaming deep reinforcement learning, we study reward centering in episodic problems and propose a generalization of differential TD. We prove that this generalization maintains the ordering of policies in the presence of termination, and thus extends differential TD to episodic problems. We show equivalence with a form of linear TD, thereby inheriting theoretical guarantees that have been shown for those algorithms. We then extend several streaming reinforcement learning algorithms to their differential counterparts. Across a range of base algorithms and environments, we empirically validate that reward centering can improve sample efficiency in episodic problems.

Reinforcement learning has achieved remarkable success in robot learning. However, under challenging exploration and contact-rich dynamics, early-stage training is frequently dominated by premature terminations such as collisions and falls. As a result, learning is overwhelmed by short-horizon, low-return trajectories, which hinder convergence and limit long-horizon exploration. To alleviate this issue, we propose a technique called Failure Episodic Memory Alert (FEMA). FEMA explicitly stores short-horizon failure experiences through an episodic memory module. During interactions, it retrieves similar failure experiences and prevents the robot from recurrently relapsing into unstable states, guiding the policy toward long-horizon trajectories with greater long-term value. FEMA can be combined easily with model-free reinforcement learning algorithms, and yields a substantial sample-efficiency improvement of 33.11% on MuJoCo tasks across several classical RL algorithms. Furthermore, integrating FEMA into a parallelized PPO training pipeline demonstrates its effectiveness on a real-world bipedal robot task.

Reinforcement learning (RL) remains fundamentally limited by poor data efficiency and weak generalization. Prior episodic RL methods attempt to alleviate this via external memory modules, yet they suffer from two key limitations: a representation bottleneck caused by shallow encoders, and a retrieval dilemma where episodic memory is accessed indiscriminately. To address these challenges, we propose Agentic Episodic Control (AEC), a novel architecture that integrates large language models (LLMs) into episodic RL. AEC uses an LLM-based semantic augmenter to generate semantic representations from raw observations, and a critical state recognizer to selectively retrieve valuable experiences. This transforms memory usage from passive similarity matching into strategic, context-aware recall. Across five BabyAI-Text environments, AEC achieves 2-6x higher data efficiency than baselines and is the only method to solve complex tasks like UnlockLocal with over 90% success. It further demonstrates strong cross-task and cross-environment generalization, maintaining performance even under distribution shifts. AEC shows that combining LLM-derived priors with reinforcement learning yields more sample-efficient and adaptable agents.