However, existing offline RL methods tend to behave poorly during fine-tuning. In this paper, we study the fine-tuning problem in the context of conservative offline RL methods and we devise an approach for learning an effective initialization from offline data that also enables fast online fine-tuning capabilities.

A Partially Observable Markov Decision Process (POMDP) is a general framework for the above problem.

We propose a novel model-based offline Reinforcement Learning (RL) framework, called Adversarial Model for Offline Reinforcement Learning (ARMOR), which can robustly learn policies to improve upon an arbitrary reference policy regardless of data coverage. ARMOR is designed to optimize policies for the worst-case performance relative to the reference policy through adversarially training a Markov decision process model. In theory, we prove that ARMOR, with a well-tuned hyperparameter, can compete with the best policy within data coverage when the reference policy is supported by the data. At the same time, ARMOR is robust to hyperparameter choices: the policy learned by ARMOR, with any admissible hyperparameter, would never degrade the performance of the reference policy, even when the reference policy is not covered by the dataset.

We propose WSAC (Weighted Safe Actor-Critic), a novel algorithm for Safe Offline Reinforcement Learning (RL) under functional approximation, which can robustly optimize policies to improve upon an arbitrary reference policy with limited data coverage. WSAC is designed as a two-player Stackelberg game to optimize a refined objective function. The actor optimizes the policy against two adversarially trained value critics with small importance-weighted Bellman errors, which focus on scenarios where the actor's performance is inferior to the reference policy. In theory, we demonstrate that when the actor employs a no-regret optimization oracle, WSAC achieves a number of guarantees: $(i)$ For the first time in the safe offline RL setting, we establish that WSAC can produce a policy that outperforms {\bf any} reference policy while maintaining the same level of safety, which is critical to designing a safe algorithm for offline RL. $(ii)$ WSAC achieves the optimal statistical convergence rate of $1/\sqrt{N}$ to the reference policy, where $N$ is the size of the offline dataset.

However, existing algorithms and theories for learning near-optimal policies in these two settings are rather different and disconnected. Towards bridging this gap, this paper initiates the theoretical study of *policy finetuning*, that is, online RL where the learner has additional access to a reference policy $\mu$ close to the optimal policy $\pi_\star$ in a certain sense. We consider the policy finetuning problem in episodic Markov Decision Processes (MDPs) with $S$ states, $A$ actions, and horizon length $H$. We first design a sharp *offline reduction* algorithm---which simply executes $\mu$ and runs offline policy optimization on the collected dataset---that finds an $\varepsilon$ near-optimal policy within $\widetilde{O}(H^3SC^\star/\varepsilon^2)$ episodes, where $C^\star$ is the single-policy concentrability coefficient between $\mu$ and $\pi_\star$. This offline result is the first that matches the sample complexity lower bound in this setting, and resolves a recent open question in offline RL. We then establish an $\Omega(H^3S\min\{C^\star, A\}/\varepsilon^2)$ sample complexity lower bound for *any* policy finetuning algorithm, including those that can adaptively explore the environment. This implies that---perhaps surprisingly---the optimal policy finetuning algorithm is either offline reduction or a purely online RL algorithm that does not use $\mu$. Finally, we design a new hybrid offline/online algorithm for policy finetuning that achieves better sample complexity than both vanilla offline reduction and purely online RL algorithms, in a relaxed setting where $\mu$ only satisfies concentrability partially up to a certain time step. Overall, our results offer a quantitative understanding on the benefit of a good reference policy, and make a step towards bridging offline and online RL.

In this paper, we study the non-asymptotic sample complexity for the pure exploration problem in contextual bandits and tabular reinforcement learning (RL): identifying an $\epsilon$-optimal policy from a set of policies $\Pi$ with high probability. Existing work in bandits has shown that it is possible to identify the best policy by estimating only the *difference* between the behaviors of individual policies-which can have substantially lower variance than estimating the behavior of each policy directly--yet the best-known complexities in RL fail to take advantage of this, and instead estimate the behavior of each policy directly. Does it suffice to estimate only the differences in the behaviors of policies in RL? We answer this question positively for contextual bandits, but in the negative for tabular RL, showing a separation between contextual bandits and RL. However, inspired by this, we show that it *almost* suffices to estimate only the differences in RL: if we can estimate the behavior of a *single* reference policy, it suffices to only estimate how any other policy deviates from this reference policy. We develop an algorithm which instantiates this principle and obtains, to the best of our knowledge, the tightest known bound on the sample complexity of tabular RL.

We propose a novel model-based offline Reinforcement Learning (RL) framework, called Adversarial Model for Offline Reinforcement Learning (ARMOR), which can robustly learn policies to improve upon an arbitrary reference policy regardless of data coverage. ARMOR is designed to optimize policies for the worst-case performance relative to the reference policy through adversarially training a Markov decision process model. In theory, we prove that ARMOR, with a well-tuned hyperparameter, can compete with the best policy within data coverage when the reference policy is supported by the data. At the same time, ARMOR is robust to hyperparameter choices: the policy learned by ARMOR, with any admissible hyperparameter, would never degrade the performance of the reference policy, even when the reference policy is not covered by the dataset.

Aligning large language models with pointwise absolute rewards has so far required online, on-policy algorithms such as PPO and GRPO. In contrast, simpler methods that can leverage offline or off-policy data, such as DPO and REBEL, are limited to learning from preference pairs or relative signals. To bridge this gap, we introduce Quantile Reward Policy Optimization (QRPO), which learns from pointwise absolute rewards while preserving the simplicity and offline applicability of DPO-like methods. QRPO uses quantile rewards to enable regression to the closed-form solution of the KL-regularized RL objective. This reward yields an analytically tractable partition function, removing the need for relative signals to cancel this term. Moreover, QRPO scales with increased compute to estimate quantile rewards, opening a new dimension for pre-computation scaling. Empirically, QRPO consistently achieves top performance on chat and coding evaluations--reward model scores, AlpacaEval 2, and LeetCode--compared to DPO, REBEL, and SimPO across diverse datasets and 8B-scale models. Finally, we find that training with robust rewards instead of converting them to preferences induces less length bias.

Large Language Models (LLMs) excel at single-turn tasks such as instruction following and summarization, yet real-world deployments require sustained multi-turn interactions where user goals and conversational context persist and evolve. A recurring challenge in this setting is context drift: the gradual divergence of a model's outputs from goal-consistent behavior across turns. Unlike single-turn errors, drift unfolds temporally and is poorly captured by static evaluation metrics. In this work, we present a study of context drift in multi-turn interactions and propose a simple dynamical framework to interpret its behavior. We formalize drift as the turn-wise KL divergence between the token-level predictive distributions of the test model and a goal-consistent reference model, and propose a recurrence model that interprets its evolution as a bounded stochastic process with restoring forces and controllable interventions. We instantiate this framework in both synthetic long-horizon rewriting tasks and realistic user-agent simulations such as in $τ$-Bench, measuring drift for several open-weight LLMs that are used as user simulators. Our experiments consistently reveal stable, noise-limited equilibria rather than runaway degradation, and demonstrate that simple reminder interventions reliably reduce divergence in line with theoretical predictions. Together, these results suggest that multi-turn drift can be understood as a controllable equilibrium phenomenon rather than as inevitable decay, providing a foundation for studying and mitigating context drift in extended interactions.

What policy should be employed in a Markov decision process with uncertain parameters? Robust optimization's answer to this question is to use rectangular