Efficient Online Linear Optimization with Approximation Algorithms

We revisit the problem of online linear optimization in case where set feasible actions is accessible through an approximated oracle with a factor α multiplicative approximation guarantee. This setting particular interesting because it captures natural extensions well-studied offline problems that are NP-hard yet admit efficient algorithms. The goal here to minimize α-regret, which extension this standard regret learning. present new algorithms significantly improved complexity for both full-information and bandit variants problem. Mainly, variants, we α-regret bounds [Formula: see text], were T number prediction rounds, using only text] calls per iteration, on average. These first results obtain average (or even polylogarithmic T) -regret bound constant c > 0 variants.