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AnExponentialLowerBoundforLinearly-Realizable MDPswithConstantSuboptimalityGap

Neural Information Processing Systems

A fundamental question in the theory of reinforcement learning is: suppose the optimalQ-function lies inthe linear span ofagivenddimensional feature mapping, is sample-efficient reinforcement learning (RL) possible? The recent and remarkable result of Weisz et al. (2020) resolves this question in the negative, providinganexponential(ind)samplesizelowerbound,whichholdsevenifthe agent has access to a generative model of the environment. One may hope that such a lower can be circumvented with an even stronger assumption that there isaconstant gapbetween the optimalQ-value ofthe best action and that ofthe second-best action (for allstates); indeed, the construction inWeisz etal.



Near-OptimalPrivateandScalablek-Clustering

Neural Information Processing Systems

Over the last decade, the leakage of private information by machine learning and data mining algorithms has had dramatic consequences, from losses of billions of dollars [60] to even costing humanlives[8].