In this paper, we propose a new algorithm for solving convex-concave saddle-point problems using regret minimization in the repeated game framework. To do so, introduce Conic Blackwell Algorithm + ([Formula: see text]), parameter- and scale-free minimizer general convex compact sets. [Formula: text] is based on approachability attains regret. We show how to efficiently instantiate many decision...

We present an algorithm for the statistical learning setting with a bounded expconcave loss in d dimensions that obtains excess risk O(d log(1/δ)/n) with probability 1−δ. The core technique is to boost the confidence of recent in-expectation O(d/n) excess risk bounds for empirical risk minimization (ERM), without sacrificing the rate, by leveraging a Bernstein condition which holds due to exp-c...

We present a novel notion of complexity that interpolates between and generalizes some classic existing complexity notions in learning theory: for estimators like empirical risk minimization (ERM) with arbitrary bounded losses, it is upper bounded in terms of data-independent Rademacher complexity; for generalized Bayesian estimators, it is upper bounded by the data-dependent information comple...

This work characterizes the generalization ability of algorithms whose predictions are linear in the input vector. To this end, we provide sharp bounds for Rademacher and Gaussian complexities of (constrained) linear classes, which directly lead to a number of generalization bounds. This derivation provides simplified proofs of a number of corollaries including: risk bounds for linear predictio...

We present a spectral approach to design approximation algorithms for network problems. observe that the underlying mathematical questions are rounding problems, which were studied in sparsification and discrepancy theory. extend these results incorporate additional non-negative linear constraints, show they can be used significantly scope of problems solved. Our algorithm is an iterative rando...

A seminal study showed repeated games with vector payoffs, which has had wide-ranging applications to decision making under uncertainty. Although this characterized the achievable guarantees in such long-run average payoff criterion, characterization and computation of these discounted criterion have remained a significant gap literature. In “An Approximate Dynamic Programming Approach Repeated...

We present a local search framework to design and analyze both combinatorial algorithms rounding for experimental problems. This provides unifying approach match improve all known results in D/A/E-design obtain new previously unknown settings. For algorithms, we provide analysis of the classical Fedorov's exchange method. prove that this simple algorithm works well as long there exists an almos...