Optimal No-regret Learning in Repeated First-price Auctions

We study online learning in repeated first-price auctions with censored feedback, where a bidder, only observing the winning bid at the end of each auction, learns to adaptively bid in order to maximize her cumulative payoff. To achieve this goal, the bidder faces a challenging dilemma: if she wins the bid--the only way to achieve positive payoffs--then she is not able to observe the highest bid of the other bidders, which we assume is iid drawn from an unknown distribution. This dilemma, despite being reminiscent of the exploration-exploitation trade-off in contextual bandits, cannot directly be addressed by the existing UCB or Thompson sampling algorithms in that literature, mainly because contrary to the standard bandits setting, when a positive reward is obtained here, nothing about the environment can be learned. In this paper, by exploiting the structural properties of first-price auctions, we develop the first learning algorithm that achieves $O(\sqrt{T}\log^2 T)$ regret bound when the bidder's private values are stochastically generated. We do so by providing an algorithm on a general class of problems, which we call monotone group contextual bandits, where the same regret bound is established under stochastically generated contexts. Further, by a novel lower bound argument, we characterize an $\Omega(T^{2/3})$ lower bound for the case where the contexts are adversarially generated, thus highlighting the impact of the contexts generation mechanism on the fundamental learning limit. Despite this, we further exploit the structure of first-price auctions and develop a learning algorithm that operates sample-efficiently (and computationally efficiently) in the presence of adversarially generated private values. We establish an $O(\sqrt{T}\log^3 T)$ regret bound for this algorithm, hence providing a complete characterization of optimal learning guarantees for this problem

CA1-projecting subiculum neurons facilitate object-place learning.

Recent anatomical evidence suggests a functionally significant back-projection pathway from the subiculum to the CA1. Here we show that the afferent circuitry of CA1-projecting subicular neurons is biased by inputs from CA1 inhibitory neurons and the visual cortex, but lacks input from the entorhinal cortex. Efferents of the CA1-projecting subiculum neurons also target the perirhinal cortex, an area strongly implicated in object-place learning. We identify a critical role for CA1-projecting subicular neurons in object-location learning and memory, and show that this projection modulates place-specific activity of CA1 neurons and their responses to displaced objects. Together, these experiments reveal a novel pathway by which cortical inputs, particularly those from the visual cortex, reach the hippocampal output region CA1. Our findings also implicate this circuitry in the formation of complex spatial representations and learning of object-place associations