The Elliptical Potential Lemma for General Distributions with an Application to Linear Thompson Sampling. (arXiv:2102.07987v3 [stat.ML] UPDATED)

In this note, we introduce a general version of the well-known elliptical
potential lemma that is a widely used technique in the analysis of algorithms
in sequential learning and decision-making problems. We consider a stochastic
linear bandit setting where a decision-maker sequentially chooses among a set
of given actions, observes their noisy rewards, and aims to maximize her
cumulative expected reward over a decision-making horizon. The elliptical
potential lemma is a key tool for quantifying uncertainty in estimating
parameters of …

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