Orthogonal Function Representations for Continuous Armed Bandits

Davide Maran, Marcello Restelli

Primary Area: reinforcement learning

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Keywords: Continuous armed bandit, Orthogonal functions, Linear bandits, Smoothness

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TL;DR: In this paper we use orthogonal functions to design two efficient algorithms for the countinuous armed bandit problem.

Abstract:

This paper addresses the continuous-armed bandit problem, which is a generalization of the standard bandit problem where the action space is a d−dimensional
hypercube $X = [−1, 1]^d$ and the reward is an s−times differentiable function
$f : \mathcal X → \mathbb R$. Traditionally, this problem is solved by assuming an implicit feature
representation in a Reproducing Kernel Hilbert Space (RKHS), where the objective
function is linear in this transformation of $\mathcal X$ . In addition to this additional intake,
this comes at the cost of overwhelming computational complexity. In contrast, we
propose an explicit representation using an orthogonal feature map (Fourier, Legendre) to reduce the problem to a linear bandit with misspecification. As a result,
we develop two algorithms _OB-LinUCB_ and _OB-PE_, achieving state-of-the-art
performance in terms of regret and computational complexity.

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Submission Number: 1798