Dual Averaging on Compactly-Supported Distributions And Application to No-Regret Learning on a Continuum
(1504.07720)Abstract
We consider an online learning problem on a continuum. A decision maker is given a compact feasible set $S$, and is faced with the following sequential problem: at iteration~$t$, the decision maker chooses a distribution $x{(t)} \in \Delta(S)$, then a loss function $\ell{(t)} : S \to \mathbb{R}+$ is revealed, and the decision maker incurs expected loss $\langle \ell{(t)}, x{(t)} \rangle = \mathbb{E}{s \sim x{(t)}} \ell{(t)}(s)$. We view the problem as an online convex optimization problem on the space $\Delta(S)$ of Lebesgue-continnuous distributions on $S$. We prove a general regret bound for the Dual Averaging method on $L2(S)$, then prove that dual averaging with $\omega$-potentials (a class of strongly convex regularizers) achieves sublinear regret when $S$ is uniformly fat (a condition weaker than convexity).
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.