Dual Averaging on Compactly-Supported Distributions And Application to No-Regret Learning on a Continuum

29 Apr 2015Walid Krichene

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 $\langle \ell^{(t)}, x^{(t)} \rangle = \mathbb{E}_{s \sim x^{(t)}} \ell^{(t)}(s)$... (read more)

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