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I address how to learn bidding strategies in repeated second-price auctions when valuations evolve over time and only aggregated feedback is revealed. In many real systems, a bidder’s value rises with the time since their last win, forcing them to trade off winning now versus maintaining future value—all while key parameters are unknown and must be inferred.
Using ideas from optimal control, differential equations, auction theory, and learning, I show how this problem captures several core issues faced by contemporary autobidders and why it provides a useful framework for their design.