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### Curiosity Killed the Cat and the Asymptotically Optimal Agent

Reinforcement learners are agents that learn to pick actions that lead to high reward. Ideally, the value of a reinforcement learner's policy approaches optimality--where the optimal informed policy is the one which maximizes reward. Unfortunately, we show that if an agent is guaranteed to be "asymptotically optimal" in any (stochastically computable) environment, then subject to an assumption about the true environment, this agent will be either destroyed or incapacitated with probability 1; both of these are forms of traps as understood in the Markov Decision Process literature. Environments with traps pose a well-known problem for agents, but we are unaware of other work which shows that traps are not only a risk, but a certainty, for agents of a certain caliber. Much work in reinforcement learning uses an ergodicity assumption to avoid this problem. Often, doing theoretical research under simplifying assumptions prepares us to provide practical solutions even in the absence of those assumptions, but the ergodicity assumption in reinforcement learning may have led us entirely astray in preparing safe and effective exploration strategies for agents in dangerous environments. Rather than assuming away the problem, we present an agent with the modest guarantee of approaching the performance of a mentor, doing safe exploration instead of reckless exploration.

### 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.

### 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.

### Categorizing Wireheading in Partially Embedded Agents

$\textit{Embedded agents}$ are not explicitly separated from their environment, lacking clear I/O channels. Such agents can reason about and modify their internal parts, which they are incentivized to shortcut or $\textit{wirehead}$ in order to achieve the maximal reward. In this paper, we provide a taxonomy of ways by which wireheading can occur, followed by a definition of wirehead-vulnerable agents. Starting from the fully dualistic universal agent AIXI, we introduce a spectrum of partially embedded agents and identify wireheading opportunities that such agents can exploit, experimentally demonstrating the results with the GRL simulation platform AIXIjs. We contextualize wireheading in the broader class of all misalignment problems - where the goals of the agent conflict with the goals of the human designer - and conjecture that the only other possible type of misalignment is specification gaming. Motivated by this taxonomy, we define wirehead-vulnerable agents as embedded agents that choose to behave differently from fully dualistic agents lacking access to their internal parts.

### 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.