We give efficient “collaboration protocols” through which two parties, who observe different features about the same instances, can interact to arrive at predictions that are more accurate than either could have obtained on their own. The parties only need to iteratively share and update their own label predictions—without either party ever having to share the actual features that they observe. Our protocols are efficient reductions to the problem of learning on each party’s feature space alone, and so can be used even in settings in which each party’s feature space is illegible to the other—which arises in models of human/AI interaction and in multi-modal learning. The communication requirements of our protocols are independent of the dimensionality of the data. In an online adversarial setting we show how to give regret bounds on the predictions that the parties arrive at with respect to a class of benchmark policies defined on the joint feature space of the two parties, despite the fact that neither party has access to this joint feature space. We also give simpler algorithms for the same task in the “batch” setting in which we assume that there is a fixed but unknown data distribution. We generalize our protocols to a decision theoretic setting with high dimensional outcome spaces—the parties in this setting do not need to communicate their (high dimensional) predictions about the outcome, but can instead communicate only “best response actions” with respect to a known utility function and their predicted outcome distribution.

Swap regret is a notion that has proven itself to be central to the study of general-sum normal-form games, with swap-regret minimization leading to convergence to the set of correlated equilibria and guaranteeing non-manipulability against a self-interested opponent. However, the situation for more general classes of games - such as Bayesian games and extensive-form games - is less clear-cut, with multiple candidate definitions for swap-regret but no known efficiently minimizable variant of swap regret that implies analogous non-manipulability guarantees.

We consider the problem of a learning agent who has to repeatedly play a general sum game against a strategic opponent who acts to maximize their own payoff by optimally responding against the learner's algorithm. The learning agent knows their own payoff function, but is uncertain about the payoff of their opponent (knowing only that it is drawn from some distribution D). What learning algorithm should the agent run in order to maximize their own total utility, either in expectation or in the worst-case over D?

Blasiok et al. [2023] proposed distance to calibration as a natural measure of calibration error that unlike expected calibration error (ECE) is continuous. Recently, Qiao and Zheng [2024] (COLT 2024) gave a nonconstructive argument establishing the existence of a randomized online predictor that can obtain distance to calibration in expectation in the adversarial setting, which is known to be impossible for ECE. They leave as an open problem finding an explicit, efficient, deterministic algorithm. We resolve this problem and give an extremely simple, efficient, deterministic algorithm that obtains distance to calibration error at most .

We study the problem of characterizing optimal learning algorithms for playing repeated games against an adversary with unknown payoffs. In this problem, the first player (called the learner) commits to a learning algorithm against a second player (called the optimizer), and the optimizer best-responds by choosing the optimal dynamic strategy for their (unknown but well-defined) payoff. Classic learning algorithms (such as no-regret algorithms) provide some counterfactual guarantees for the learner, but might perform much more poorly than other learning algorithms against particular optimizer payoffs.

We study a repeated contracting setting in which a Principal adaptively chooses amongst k Agents at each of T rounds. The Agents are non-myopic, and so a mechanism for the Principal induces a T-round extensive form game amongst the Agents. We give several results aimed at understanding an under-explored aspect of contract theory --- the game induced when choosing an Agent to contract with. First, we show that this game admits a pure-strategy non-responsive equilibrium amongst the Agents --- informally an equilibrium in which the Agent's actions depend on the history of realized states of nature, but not on the history of each other's actions, and so avoids the complexities of collusion and threats. Next, we show that if the Principal selects Agents using a monotone bandit algorithm, then for any concave contract, in any such equilibrium, the Principal obtains no regret to contracting with the best Agent in hindsight --- not just given their realized actions, but also to the counterfactual world in which they had offered a guaranteed T-round contract to the best Agent in hindsight, which would have induced a different sequence of actions. Finally, we show that if the Principal selects Agents using a monotone bandit algorithm which guarantees no swap-regret, then the Principal can additionally offer only limited liability contracts (in which the Agent never needs to pay the Principal) while getting no-regret to the counterfactual world in which she offered a linear contract to the best Agent in hindsight --- despite the fact that linear contracts are not limited liability. We instantiate this theorem by demonstrating the existence of a monotone no swap-regret bandit algorithm, which to our knowledge has not previously appeared in the literature.

We study a repeated Principal Agent problem between a long lived Principal and Agent pair in a prior free setting. In our setting, the sequence of realized states of nature may be adversarially chosen, the Agent is non-myopic, and the Principal aims for a strong form of policy regret. Following [Camara et al., 2020], we model the Agent's long-run behavior with behavioral assumptions that relax the common prior assumption (for example, that the Agent has no swap regret). Within this framework, we revisit the mechanism proposed by [Camara et al., 2020], which informally uses calibrated forecasts of the unknown states of nature in place of a common prior. We give two main improvements. First, we give a mechanism that has an exponentially improved dependence (in terms of both running time and regret bounds) on the number of distinct states of nature. To do this, we show that our mechanism does not require truly calibrated forecasts, but rather forecasts that are unbiased subject to only a polynomially sized collection of events --- which can be produced with polynomial overhead. Second, instead of constructing a policy and assuming that the policy is "stable" (informally requiring that under such a policy, all approximately optimal actions lead to approximately the same Principal payoff), we propose a general framework given access to a stable policy oracle. We then instantiate the oracle by developing efficient algorithms in several significant special cases, including the focal linear contracting setting. Taken together, our new mechanism makes the compelling framework proposed by [Camara et al., 2020] more powerful, now able to be realized over polynomially sized state spaces.

We consider a revenue-maximizing single seller with mitems for sale to a single buyer whose value v(·) for the items is drawn from a known distribution Dof support k. A series of works by Cai et al. establishes that when each v(·) in the support of Dis additive or unit-demand (or c-demand), the revenue-optimal auction can be found in poly(m,k) time.