Budget constraints in repeated auctions require the optimizer to switch among up to k+1 mixed strategies over time, and a proportional controller for the learner makes the optimizer's utility no higher than the budgeted Stackelberg equilibrium value.
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Learning vs. Optimizing Bidders in Budgeted Auctions
Budget constraints in repeated auctions require the optimizer to switch among up to k+1 mixed strategies over time, and a proportional controller for the learner makes the optimizer's utility no higher than the budgeted Stackelberg equilibrium value.