Nicolò Cesa-Bianchi

In machine learning, a field addressing the extraction of information and structure from finite data with the means of computer science and mathematics, maps from finite-dimensional spaces of data or computations into spaces of higher, or infinite dimensionality are a central theme. The workshop brought together researchers with diverse viewpoints to discuss how different theoretical sub-communities within the field treat the resulting ill-posed operations, and what kind of features of algorithms and models can emerge as a result.

We study the problem of regret minimization for a single bidder in a sequence of first-price auctions where the bidder discovers the item’s value only if the auction is won. Our main contribution is a complete characterization, up to logarithmic factors, of the minimax regret in terms of the auction’s transparency, which controls the amount of information on competing bids disclosed by the auctioneer at the end of each auction. Our results hold under different assumptions (stochastic, adversarial, and their smoothed variants) on the environment generating the bidder’s valuations and competing bids. These minimax rates reveal how the interplay between transparency and the nature of the environment affects how fast one can learn to bid optimally in first-price auctions.

This work addresses the mediator feedback problem, a bandit game where the decision set consists of a number of policies, each associated with a probability distribution over a common space of outcomes. Upon choosing a policy, the learner observes an outcome sampled from its distribution and incurs the loss assigned to this outcome in the present round. We introduce the policy set capacity as an information-theoretic measure for the complexity of the policy set. Adopting the classical EXP4 algorithm, we provide new regret bounds depending on the policy set capacity in both the adversarial and the stochastic settings. For a selection of policy set families, we prove nearly-matching lower bounds, scaling similarly with the capacity. We also consider the case when the policies' distributions can vary between rounds, thus addressing the related bandits with expert advice problem, which we improve upon its prior results. Additionally, we prove a lower bound showing that exploiting the similarity between the policies is not possible in general under linear bandit feedback. Finally, for a full-information variant, we provide a regret bound scaling with the information radius of the policy set.

Multitask learning is a powerful framework that enables one to simultaneously learn multiple related tasks by sharing information between them. Quantifying uncertainty in the estimated tasks is of pivotal importance for many downstream applications, such as online or active learning. In this work, we provide novel multitask confidence intervals in the challenging agnostic setting, i.e., when neither the similarity between tasks nor the tasks' features are available to the learner. The obtained intervals do not require i.i.d. data and can be directly applied to bound the regret in online learning. Through a refined analysis of the multitask information gain, we obtain new regret guarantees that, depending on a task similarity parameter, can significantly improve over treating tasks independently. We further propose a novel online learning algorithm that achieves such improved regret without knowing this parameter in advance, i.e., automatically adapting to task similarity. As a second key application of our results, we introduce a novel multitask active learning setup where several tasks must be simultaneously optimized, but only one of them can be queried for feedback by the learner at each round. For this problem, we design a no-regret algorithm that uses our confidence intervals to decide which task should be queried. Finally, we empirically validate our bounds and algorithms on synthetic and real-world (drug discovery) data.