Brittany Gelb

Introduction In this post, we introduce contributions and supracontributions[1], which are basic objects from infra-Bayesianism that go beyond the crisp case (the case of credal sets). We then define supra-POMDPs, a generalization of partially observable Markov decision processes (POMDPs). This generalization has state transition dynamics that are described by supracontributions....

This proof section accompanies Formalizing Newcombian problems with fuzzy infra-Bayesianism. We prove the following result. > Theorem [Alexander Appel (@Diffractor), Vanessa Kosoy (@Vanessa Kosoy)]: > > Let ν:ΠH×O<H→ΔO be a Newcombian problem of horizon H∈N that satisfies pseudocausality. Let Mν=(S,Θ0,A,O,T,B) denote the associated supra-POMDP with infinite time horizon and time...

This post accompanies Crisp Supra-Decision Processes and contains the proof of the following proposition. > Proposition 1 [Alexander Appel (@Diffractor), Vanessa Kosoy (@Vanessa Kosoy)]: Let M=(S,s0,A,O,T,B,L,γ) be a crisp supra-MDP with geometric time discount such that S and A are finite. Then there exists a stationary optimal policy. Proof: We...

Introduction In this post, we describe a generalization of Markov decision processes (MDPs) and partially observable Markov decision processes (POMDPs) called crisp supra-MDPs and supra-POMDPs. The new feature of these decision processes is that the stochastic transition dynamics are multivalued, i.e. specified by credal sets. We describe how supra-MDPs give...

Introduction Credal sets, a special case of infradistributions[1] in infra-Bayesianism and classical objects in imprecise probability theory, provide a means of describing uncertainty without assigning exact probabilities to events as in Bayesianism. This is significant because as argued in the introduction to this sequence, Bayesianism is inadequate as a framework...

This post accompanies An Introduction to Credal Sets and Infra-Bayes Learnability. Notation We use ΔX to denote the space of probability distributions over a set X, which is assumed throughout to be a compact metric space. We use □X to denote the set of credal sets over X. Given f:X→R...

Introduction This post accompanies An Introduction to Reinforcement Learning for Understanding Infra-Bayesianism. The goal of this introduction is to provide a high-level overview of the proofs contained in this post. The proof of Proposition 1 is achieved through three lemmas. I believe the most insightful part of the proof is...