We study sample efficient reinforcement learning (RL) under the general framework of interactive decision making, which includes Markov decision process (MDP), partially observable Markov decision process (POMDP), and predictive state representation (PSR) as special cases. Toward finding the minimum assumption that empowers sample efficient learning, we propose a novel complexity measure, generalized eluder coefficient (GEC), which characterizes the fundamental tradeoff between exploration and exploitation in online interactive decision making. In specific, GEC captures the hardness of exploration by comparing the error of predicting the performance of the updated policy with the in-sample training error evaluated on the historical data. We show that RL problems with low GEC form a remarkably rich class, which subsumes low Bellman eluder dimension problems, bilinear class, low witness rank problems, PO-bilinear class, and generalized regular PSR, where generalized regular PSR, a new tractable PSR class identified by us, includes nearly all known tractable POMDPs. Furthermore, in terms of algorithm design, we propose a generic posterior sampling algorithm, which can be implemented in both model-free and model-based fashion, under both fully observable and partially observable settings. The proposed algorithm modifies the standard posterior sampling algorithm in two aspects: (i) we use an optimistic prior distribution that biases towards hypotheses with higher values and (ii) a loglikelihood function is set to be the empirical loss evaluated on the historical data, where the choice of loss function supports both model-free and model-based learning. We prove that the proposed algorithm is sample efficient by establishing a sublinear regret upper bound in terms of GEC. In summary, we provide a new and unified understanding of both fully observable and partially observable RL.

我们研究了基于互动决策制定的样本有效强化学习，提出了广义Eluder系数作为复杂度度量，并通过后验采样算法在完全可观察和部分可观察的环境下实现模型自由和模型为基础的学习，在探索和开发之间建立了基本权衡。

GEC：MDP、POMDP及更广泛情境下交互式决策的统一框架