Making good decisions in partially observable and non-deterministic scenarios is a crucial capability for robots. APartially Observable Markov Decision Process (POMDP) is a general framework for the above problem. Despite advances in POMDP solving, problems with long planning horizons and evolving environments remain difficult to solve even by the best approximate solvers today. To alleviate this difficulty, we propose a slightly modified POMDP problem, called a ReferenceBased POMDP, where the objective is to balance between maximizing the expected total reward and being close to a given reference (stochastic) policy. The optimal policy of a Reference-Based POMDP can be computed via iterative expectations using the given reference policy, thereby avoiding exhaustive enumeration of actions at each belief node of the search tree. We demonstrate theoretically that the standard POMDP under stochastic policies is related to the Reference-Based POMDP. To demonstrate the feasibility of exploiting the formulation, we present a basic algorithm REFSOLVER. Results from experiments on long-horizon navigation problems indicate that this basic algorithm substantially outperforms POMCP.

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.

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.

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.

Unfortunately, behavior regularization, a simple yet effective offline RL algorithm, tends to struggle in this regard.

However, state-of-the-art (SOT A) RL techniques with Temporal-Difference (TD) learning frameworks often suffer from learning inefficiency, due to the significant expansion of the augmented state space with the delay. To improve learning efficiency without sacrificing performance, this work introduces a novel framework called V ariational Delayed Policy Optimization (VDPO), which reformulates delayed RL as a variational inference problem. This problem is further modelled as a two-step iterative optimization problem, where the first step is TD learning in the delay-free environment with a small state space, and the second step is behaviour cloning which can be addressed much more efficiently than TD learning. We not only provide a theoretical analysis of VDPO in terms of sample complexity and performance, but also empirically demonstrate that VDPO can achieve consistent performance with SOT A methods, with a significant enhancement of sample efficiency (approximately 50% less amount of samples) in the MuJoCo benchmark.

What policy should be employed in a Markov decision process with uncertain parameters?