A Theory of Bounded Inductive Rationality

TL;DR

This paper develops a new theory of rational decision making for agents with limited computational abilities, addressing logical omniscience assumptions and analyzing strategic interactions among such agents.

Contribution

It introduces a boundedly rational inductive framework that allows agents to learn and adapt without assuming full logical omniscience, including a folk theorem for strategic interactions.

Findings

Agents learn to value random lotteries at expected rewards.

Bounded rational agents can converge to stable strategies in strategic settings.

Theory applies to decision problems like betting on digits of pi and game interactions.

Abstract

The dominant theories of rational choice assume logical omniscience. That is, they assume that when facing a decision problem, an agent can perform all relevant computations and determine the truth value of all relevant logical/mathematical claims. This assumption is unrealistic when, for example, we offer bets on remote digits of pi or when an agent faces a computationally intractable planning problem. Furthermore, the assumption of logical omniscience creates contradictions in cases where the environment can contain descriptions of the agent itself. Importantly, strategic interactions as studied in game theory are decision problems in which a rational agent is predicted by its environment (the other players). In this paper, we develop a theory of rational decision making that does not assume logical omniscience. We consider agents who repeatedly face decision problems (including ones like betting on digits of pi or games against other agents). The main contribution of this paper is to provide a sensible theory of rationality for such agents. Roughly, we require that a boundedly rational inductive agent tests each efficiently computable hypothesis infinitely often and follows those hypotheses that keep their promises of high rewards. We then prove that agents that are rational in this sense have other desirable properties. For example, they learn to value random and pseudo-random lotteries at their expected reward. Finally, we consider strategic interactions between different agents and prove a folk theorem for what strategies bounded rational inductive agents can converge to.