# A Theory of Bounded Inductive Rationality

arXiv: https://arxiv.org/abs/2307.05068 · HTML: https://mlsanity.com/paper/2307.05068/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 57 references that are in the map.
- First posted on arXiv 11 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [Embedded Agency](https://mlsanity.com/paper/1902.09469/) (2019)
- [What is Decidable about Partially Observable Markov Decision Processes with ω-Regular Objectives](https://mlsanity.com/paper/1309.2802/) (2013)
- [Robust Cooperation in the Prisoner's Dilemma: Program Equilibrium via Provability Logic](https://mlsanity.com/paper/1401.5577/) (2014)
- [Parametric Bounded L"ob's Theorem and Robust Cooperation of Bounded Agents](https://mlsanity.com/paper/1602.04184/) (2016)
- [A Formal Approach to the Problem of Logical Non-Omniscience](https://mlsanity.com/paper/1707.08747/) (2017)
- [Temporal Inference with Finite Factored Sets](https://mlsanity.com/paper/2109.11513/) (2021)

## Built on by (most cited first, 1 of 1)

- [Market-based Architectures in RL and Beyond](https://mlsanity.com/paper/2503.05828/) (2025)

## Abstract (arXiv)

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.