Reconciling Rewards with Predictive State Representations

Predictive state representations (PSRs) are models of controlled non-Markov observation sequences which exhibit the same generative process governing POMDP observations without relying on an underlying latent state. In that respect, a PSR is indistinguishable from the corresponding POMDP. However, PSRs notoriously ignore the notion of rewards, which undermines the general utility of PSR models for control, planning, or reinforcement learning. Therefore, we describe a sufficient and necessary accuracy condition which determines whether a PSR is able to accurately model POMDP rewards, we show that rewards can be approximated even when the accuracy condition is not satisfied, and we find that a non-trivial number of POMDPs taken from a well-known third-party repository do not satisfy the accuracy condition. We propose reward-predictive state representations (R-PSRs), a generalization of PSRs which accurately models both observations and rewards, and develop value iteration for R-PSRs. We show that there is a mismatch between optimal POMDP policies and the optimal PSR policies derived from approximate rewards. On the other hand, optimal R-PSR policies perfectly match optimal POMDP policies, reconfirming R-PSRs as accurate state-less generative models of observations and rewards.

Detecting Changes and Avoiding Catastrophic Forgetting in Dynamic Partially Observable Environments

The ability of an agent to detect changes in an environment is key to successful adaptation. This ability involves at least two phases: learning a model of an environment, and detecting that a change is likely to have occurred when this model is no longer accurate. This task is particularly challenging in partially observable environments, such as those modeled with partially observable Markov decision processes (POMDPs). Some predictive learners are able to infer the state from observations and thus perform better with partial observability. Predictive state representations (PSRs) and neural networks are two such tools that can be trained to predict the probabilities of future observations. However, most such existing methods focus primarily on static problems in which only one environment is learned. In this paper, we propose an algorithm that uses statistical tests to estimate the probability of different predictive models to fit the current environment. We exploit the underlying probability distributions of predictive models to provide a fast and explainable method to assess and justify the model's beliefs about the current environment. Crucially, by doing so, the method can label incoming data as fitting different models, and thus can continuously train separate models in different environments. This new method is shown to prevent catastrophic forgetting when new environments, or tasks, are encountered. The method can also be of use when AI-informed decisions require justifications because its beliefs are based on statistical evidence from observations. We empirically demonstrate the benefit of the novel method with simulations in a set of POMDP environments.