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The prior independent framework for algorithm design considers how well an algorithm that does not know the distribution of its inputs approximates the expected performance of the optimal algorithm for this distribution. This paper gives a method that is agnostic to problem setting for proving lower bounds on the prior independent approximation factor of any algorithm. The method constructs a correlated distribution over inputs that can be generated both as a distribution over i.i.d. good-for-algorithms distributions and as a distribution over i.i.d. bad-for-algorithms distributions. Prior independent algorithms are upper-bounded by the optimal algorithm for the latter distribution even when the true distribution is the former. Thus, the ratio of the expected performances of the Bayesian optimal algorithms for these two decompositions is a lower bound on the prior independent approximation ratio. The techniques of the paper connect prior independent algorithm design, Yaos Minimax Principle, and information design. We apply this framework to give new lower bounds on several canonical prior independent mechanism design problems.
While recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a convex function
We study social choice rules under the utilitarian distortion framework, with an additional metric assumption on the agents costs over the alternatives. In this approach, these costs are given by an underlying metric on the set of all agents plus alt
We study the problem of PAC learning one-hidden-layer ReLU networks with $k$ hidden units on $mathbb{R}^d$ under Gaussian marginals in the presence of additive label noise. For the case of positive coefficients, we give the first polynomial-time algo
The problem of scheduling unrelated machines by a truthful mechanism to minimize the makespan was introduced in the seminal Algorithmic Mechanism Design paper by Nisan and Ronen. Nisan and Ronen showed that there is a truthful mechanism that provides
This paper compares two leading approaches for robust optimization in the models of online algorithms and mechanism design. Competitive analysis compares the performance of an online algorithm to an offline benchmark in worst-case over inputs, and pr