Part of Advances in Neural Information Processing Systems 30 (NIPS 2017)
arthur flajolet, Patrick Jaillet
We consider the problem of repeated bidding in online advertising auctions when some side information (e.g. browser cookies) is available ahead of submitting a bid in the form of a $d$-dimensional vector. The goal for the advertiser is to maximize the total utility (e.g. the total number of clicks) derived from displaying ads given that a limited budget $B$ is allocated for a given time horizon $T$. Optimizing the bids is modeled as a contextual Multi-Armed Bandit (MAB) problem with a knapsack constraint and a continuum of arms. We develop UCB-type algorithms that combine two streams of literature: the confidence-set approach to linear contextual MABs and the probabilistic bisection search method for stochastic root-finding. Under mild assumptions on the underlying unknown distribution, we establish distribution-independent regret bounds of order $\tilde{O}(d \cdot \sqrt{T})$ when either $B = \infty$ or when $B$ scales linearly with $T$.