934 research outputs found
Self-Optimizing and Pareto-Optimal Policies in General Environments based on Bayes-Mixtures
The problem of making sequential decisions in unknown probabilistic
environments is studied. In cycle action results in perception
and reward , where all quantities in general may depend on the complete
history. The perception and reward are sampled from the (reactive)
environmental probability distribution . This very general setting
includes, but is not limited to, (partial observable, k-th order) Markov
decision processes. Sequential decision theory tells us how to act in order to
maximize the total expected reward, called value, if is known.
Reinforcement learning is usually used if is unknown. In the Bayesian
approach one defines a mixture distribution as a weighted sum of
distributions \nu\in\M, where \M is any class of distributions including
the true environment . We show that the Bayes-optimal policy based
on the mixture is self-optimizing in the sense that the average value
converges asymptotically for all \mu\in\M to the optimal value achieved by
the (infeasible) Bayes-optimal policy which knows in advance. We
show that the necessary condition that \M admits self-optimizing policies at
all, is also sufficient. No other structural assumptions are made on \M. As
an example application, we discuss ergodic Markov decision processes, which
allow for self-optimizing policies. Furthermore, we show that is
Pareto-optimal in the sense that there is no other policy yielding higher or
equal value in {\em all} environments \nu\in\M and a strictly higher value in
at least one.Comment: 15 page
BOF-UCB: A Bayesian-Optimistic Frequentist Algorithm for Non-Stationary Contextual Bandits
We propose a novel Bayesian-Optimistic Frequentist Upper Confidence Bound
(BOF-UCB) algorithm for stochastic contextual linear bandits in non-stationary
environments. This unique combination of Bayesian and frequentist principles
enhances adaptability and performance in dynamic settings. The BOF-UCB
algorithm utilizes sequential Bayesian updates to infer the posterior
distribution of the unknown regression parameter, and subsequently employs a
frequentist approach to compute the Upper Confidence Bound (UCB) by maximizing
the expected reward over the posterior distribution. We provide theoretical
guarantees of BOF-UCB's performance and demonstrate its effectiveness in
balancing exploration and exploitation on synthetic datasets and classical
control tasks in a reinforcement learning setting. Our results show that
BOF-UCB outperforms existing methods, making it a promising solution for
sequential decision-making in non-stationary environments
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