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### Strong Asymptotic Optimality in General Environments

Reinforcement Learning agents are expected to eventually perform well. Typically, this takes the form of a guarantee about the asymptotic behavior of an algorithm given some assumptions about the environment. We present an algorithm for a policy whose value approaches the optimal value with probability 1 in all computable probabilistic environments, provided the agent has a bounded horizon. This is known as strong asymptotic optimality, and it was previously unknown whether it was possible for a policy to be strongly asymptotically optimal in the class of all computable probabilistic environments. Our agent, Inquisitive Reinforcement Learner (Inq), is more likely to explore the more it expects an exploratory action to reduce its uncertainty about which environment it is in, hence the term inquisitive. Exploring inquisitively is a strategy that can be applied generally; for more manageable environment classes, inquisitiveness is tractable. We conducted experiments in "grid-worlds" to compare the Inquisitive Reinforcement Learner to other weakly asymptotically optimal agents.

### Thompson Sampling is Asymptotically Optimal in General Environments

We discuss a variant of Thompson sampling for nonparametric reinforcement learning in a countable classes of general stochastic environments. These environments can be non-Markov, non-ergodic, and partially observable. We show that Thompson sampling learns the environment class in the sense that (1) asymptotically its value converges to the optimal value in mean and (2) given a recoverability assumption regret is sublinear.

### On the Computability of Solomonoff Induction and Knowledge-Seeking

Solomonoff induction is held as a gold standard for learning, but it is known to be incomputable. We quantify its incomputability by placing various flavors of Solomonoff's prior M in the arithmetical hierarchy. We also derive computability bounds for knowledge-seeking agents, and give a limit-computable weakly asymptotically optimal reinforcement learning agent.

### Pessimism About Unknown Unknowns Inspires Conservatism

If we could define the set of all bad outcomes, we could hard-code an agent which avoids them; however, in sufficiently complex environments, this is infeasible. We do not know of any general-purpose approaches in the literature to avoiding novel failure modes. Motivated by this, we define an idealized Bayesian reinforcement learner which follows a policy that maximizes the worst-case expected reward over a set of world-models. We call this agent pessimistic, since it optimizes assuming the worst case. A scalar parameter tunes the agent's pessimism by changing the size of the set of world-models taken into account. Our first main contribution is: given an assumption about the agent's model class, a sufficiently pessimistic agent does not cause "unprecedented events" with probability $1-\delta$, whether or not designers know how to precisely specify those precedents they are concerned with. Since pessimism discourages exploration, at each timestep, the agent may defer to a mentor, who may be a human or some known-safe policy we would like to improve. Our other main contribution is that the agent's policy's value approaches at least that of the mentor, while the probability of deferring to the mentor goes to 0. In high-stakes environments, we might like advanced artificial agents to pursue goals cautiously, which is a non-trivial problem even if the agent were allowed arbitrary computing power; we present a formal solution.

### Asymptotically Optimal Agents

Artificial general intelligence aims to create agents capable of learning to solve arbitrary interesting problems. We define two versions of asymptotic optimality and prove that no agent can satisfy the strong version while in some cases, depending on discounting, there does exist a non-computable weak asymptotically optimal agent.