Emmanuel Esposito

2023

1. NeurIPS

   On the Minimax Regret for Online Learning with Feedback Graphs

   Khaled Eldowa, Emmanuel Esposito, Tommaso Cesari, and Nicolò Cesa-Bianchi

   To appear in NeurIPS ’23, 2023

   Abs arXiv

   In this work, we improve on the upper and lower bounds for the regret of online learning with strongly observable undirected feedback graphs. The best known upper bound for this problem is \mathcalO\bigl(\sqrtαT\ln K\bigr), where K is the number of actions, αis the independence number of the graph, and T is the time horizon. The \sqrt\ln K factor is known to be necessary when α= 1 (the experts case). On the other hand, when α= K (the bandits case), the minimax rate is known to be Θ\bigl(\sqrtKT\bigr), and a lower bound Ω\bigl(\sqrtαT\bigr) is known to hold for any α. Our improved upper bound \mathcalO\bigl(\sqrtαT(1+\ln(K/α))\bigr) holds for any αand matches the lower bounds for bandits and experts, while interpolating intermediate cases. To prove this result, we use FTRL with q-Tsallis entropy for a carefully chosen value of q ∈[1/2, 1) that varies with α. The analysis of this algorithm requires a new bound on the variance term in the regret. We also show how to extend our techniques to time-varying graphs, without requiring prior knowledge of their independence numbers. Our upper bound is complemented by an improved Ω\bigl(\sqrtαT(\ln K)/(\lnα)\bigr) lower bound for all α> 1, whose analysis relies on a novel reduction to multitask learning. This shows that a logarithmic factor is necessary as soon as α< K.

2. ICML

   Delayed Bandits: When Do Intermediate Observations Help?

   Emmanuel Esposito, Saeed Masoudian, Hao Qiu, Dirk van der Hoeven, Nicolò Cesa-Bianchi, and Yevgeny Seldin

   ICML ’23, 2023

   Abs arXiv HTML

   We study a K-armed bandit with delayed feedback and intermediate observations. We consider a model where intermediate observations have a form of a finite state, which is observed immediately after taking an action, whereas the loss is observed after an adversarially chosen delay. We show that the regime of the mapping of states to losses determines the complexity of the problem, irrespective of whether the mapping of actions to states is stochastic or adversarial. If the mapping of states to losses is adversarial, then the regret rate is of order \sqrt(K+d)T (within log factors), where T is the time horizon and d is a fixed delay. This matches the regret rate of a K-armed bandit with delayed feedback and without intermediate observations, implying that intermediate observations are not helpful. However, if the mapping of states to losses is stochastic, we show that the regret grows at a rate of \sqrt\bigl(K+\min{|\mathcalS|,d}\bigr)T (within log factors), implying that if the number |\mathcalS| of states is smaller than the delay, then intermediate observations help. We also provide refined high-probability regret upper bounds for non-uniform delays, together with experimental validation of our algorithms.

2022

1. NeurIPS

   Learning on the Edge: Online Learning with Stochastic Feedback Graphs

   Emmanuel Esposito, Federico Fusco, Dirk van der Hoeven, and Nicolò Cesa-Bianchi

   NeurIPS ’22, 2022

   Abs arXiv HTML

   The framework of feedback graphs is a generalization of sequential decision-making with bandit or full information feedback. In this work, we study an extension where the directed feedback graph is stochastic, following a distribution similar to the classical Erdős-Rényi model. Specifically, in each round every edge in the graph is either realized or not with a distinct probability for each edge. We prove nearly optimal regret bounds of order \min\bigl{\min_\varepsilon \sqrt(\alpha_\varepsilon/\varepsilon) T, \min_\varepsilon (\delta_\varepsilon/\varepsilon)^1/3 T^2/3\bigr} (ignoring logarithmic factors), where \alpha_\varepsilon and \delta_\varepsilon are graph-theoretic quantities measured on the support of the stochastic feedback graph \mathcalG with edge probabilities thresholded at \varepsilon. Our result, which holds without any preliminary knowledge about \mathcalG, requires the learner to observe only the realized out-neighborhood of the chosen action. When the learner is allowed to observe the realization of the entire graph (but only the losses in the out-neighborhood of the chosen action), we derive a more efficient algorithm featuring a dependence on weighted versions of the independence and weak domination numbers that exhibits improved bounds for some special cases.