Reinforcement learning (RL) problems are often phrased in terms of Markov decision processes (MDPs). In this thesis we go beyond MDPs and consider RL in environments that are non-Markovian, non-ergodic and only partially observable. Our focus is not on practical algorithms, but rather on the fundamental underlying problems: How do we balance exploration and exploitation? How do we explore optimally? When is an agent optimal? We follow the nonparametric realizable paradigm. We establish negative results on Bayesian RL agents, in particular AIXI. We show that unlucky or adversarial choices of the prior cause the agent to misbehave drastically. Therefore Legg-Hutter intelligence and balanced Pareto optimality, which depend crucially on the choice of the prior, are entirely subjective. Moreover, in the class of all computable environments every policy is Pareto optimal. This undermines all existing optimality properties for AIXI. However, there are Bayesian approaches to general RL that satisfy objective optimality guarantees: We prove that Thompson sampling is asymptotically optimal in stochastic environments in the sense that its value converges to the value of the optimal policy. We connect asymptotic optimality to regret given a recoverability assumption on the environment that allows the agent to recover from mistakes. Hence Thompson sampling achieves sublinear regret in these environments. Our results culminate in a formal solution to the grain of truth problem: A Bayesian agent acting in a multi-agent environment learns to predict the other agents' policies if its prior assigns positive probability to them (the prior contains a grain of truth). We construct a large but limit computable class containing a grain of truth and show that agents based on Thompson sampling over this class converge to play Nash equilibria in arbitrary unknown computable multi-agent environments.

本文提出了在非Markovian、非ergodic且只部分可观察的环境下进行强化学习的问题。作者建立了贝叶斯强化学习代理的负面结果，并证明Thompson采样在随机环境中是渐进最优的。此外，作者构建了一个大但可计算的类，展示了基于Thompson采样的代理在这个类中收敛于任意未知可计算多智能体环境中的纳什均衡。

非参数通用强化学习