Title: "The Divergence Test for Universal Hypothesis Testing: Beating the Generalized Likelihood Ratio Test"

Abstract:  Universal hypothesis testing refers to the binary statistical hypothesis testing problem where n independent and identically distributed random variables are either distributed according to the null hypothesis P or the alternative hypothesis Q, and only P is known. The generalized likelihood ratio test (GLRT) for this problem is the Hoeffding test, which accepts the null hypothesis if the Kullback-Leibler (KL) divergence between the empirical distribution of the observed random variables and the null hypothesis is below some threshold. In this work, we propose the divergence test, which replaces the KL divergence in the Hoeffding test by an arbitrary divergence. For this test, we derive a second-order asymptotic expansion for the probability of a false-negative when the probability of a false-positive is bounded by some fixed value (Stein’s regime). We demonstrate that when the divergence belongs to the class of invariant divergences (which includes the Rényi divergence and the f-divergence), the divergence test has the same second-order performance as the Hoeffding test. In contrast, when the divergence is non-invariant, the divergence test may outperform the Hoeffding test for some alternative hypotheses. In particular, we observe this phenomenon when the divergence is the squared Mahalanobis distance. We conclude that a hypothesis test that accepts the null hypothesis if the squared Mahalanobis distance between the empirical distribution of the observed random variables and the null hypothesis is below some threshold may outperform the GLRT. Potentially, this behavior could be exploited by a composite hypothesis test with partial knowledge of the alternative hypothesis by tailoring the squared Mahalanobis distance to the set of possible alternative hypotheses.

This is joint work with K.V. Harsha (Gandhi Institute of Technology and Management, Hyderabad, India) and Jithin Ravi (Indian Institute of Technology Kharagpur, India). 

Presentation slides

Biography: Dr. Tobias Koch received the M.Sc. (Hons.) and Ph.D. degrees in electrical engineering from ETH Zurich, Switzerland, in 2004 and 2009, respectively. From June 2010 until May 2012, he was a Marie Curie Intra-European Research Fellow with the University of Cambridge, UK. He was also a Research Intern at Bell Labs, Murray Hill, NJ, USA, in 2004, and the Universitat Pompeu Fabra, Barcelona, Spain, in 2007. He joined the Universidad Carlos III de Madrid, Spain, in 2012, where he is currently an Associate Professor. His research interests are in digital communication theory and information theory.

Dr. Koch received a Starting Grant from the European Research Council (ERC), a Ramón y Cajal Research Fellowship, a Marie Curie Intra-European Fellowship, a Marie Curie Career Integration Grant, and a Fellowship for Prospective Researchers from the Swiss National Science Foundation. He further received a medal of the 2018 Young Researchers Award “Agustín de Betancourt y Molina” by the Royal Academy of Engineering of Spain. He served as the Vice Chair for the Spain Chapter of the IEEE Information Theory Society from 2013 to 2016, and he served as the Chapter’s Chair from 2020 to 2023. Since 2020, he has been serving as an Associate Editor for Communications and Shannon Theory for the IEEE Transactions on Information Theory.

Title: "Tensor-low rank models for reinforcement learning" 

Abstract: Reinforcement Learning (RL) has emerged as a promising paradigm for addressing sequential optimization problems when the dynamics of the underlying systems are unknown. The primary objective in RL is to learn a policy that maximizes expected future rewards, or value functions. This is typically achieved through learning the optimal value functions or, alternatively, the optimal policy. The performance of RL algorithms is often limited by the choice of models used, which strongly depends on the specific problem. However, a common feature of many RL problems is that the optimal value functions and policies tend to be low rank. Motivated by this observation, this talk explores low-rank modeling as a general tool for RL problems. Specifically, we demonstrate how low-rank matrix and tensor models can approximate both value functions and policies. Additionally, we show how low-rank models can be applied to alternative setups, such as multi-task RL. This approach results in parsimonious algorithms that balance the rapid convergence of simple linear models with the high reward potential of neural networks.

Presentation slides

Biography: Dr. Antonio G. Marques received the Telecommunications Engineering degree and the Doctorate degree, both with highest honors, from Carlos III University of Madrid, Spain, in 2002 and 2007, respectively. In 2007, he became a faculty of the Department of Signal Theory and Communications, King Juan Carlos University, Madrid, Spain, where he currently develops his research and teaching activities as a full professor and director of the Data Science and Signal Processing for Networks research group. From 2005 to 2015, he held different visiting positions at the University of Minnesota, Minneapolis. In 2015, 2016 and 2017 he was a visitor scholar at the University of Pennsylvania, Philadelphia. 

His current research focuses on signal processing, machine learning, data science and artificial intelligence over graphs, and nonlinear and stochastic optimization of wireless and transportation networks, areas where he has published more than 150 papers.

Dr. Marques has served the IEEE in a number of posts, including as an associate editor and the technical / general chair of different conferences. Currently, he is a Senior Area Editor of the IEEE Trans. on Signal Process., the Technical Chair of Asilomar 2024 and the General Co-Chair of CAMSAP 2025. His work has been awarded in several journals, conferences and workshops, with recent ones including the IEEE SPS IEEE Y.A. Best Paper Award 2020, and CIT 2021. He is the recipient of the ``2020 EURASIP Early Career Award'' and a member of IEEE, EURASIP and the ELLIS society.

Title:  "Parallel predictive entropy search for multi-objective Bayesian optimization with constraints" 

Abstract: Real-world problems often involve the optimization of several objectives under multiple constraints. An example is the hyper-parameter tuning problem of machine learning algorithms. For example, minimizing both an estimate of the generalization error of a deep neural network and its prediction time. We may also consider, as a constraint, that the deep neural network must be implemented in a chip with an area below some size. Here, both the objectives and the constraint are black boxes, i.e., functions whose analytical expressions are unknown and are expensive to evaluate. Bayesian optimization (BO) methods have shown state-of-the-art results in these tasks. For this, they evaluate iteratively, at carefully chosen locations, the objectives and the constraints with the goal of solving the optimization problem in a small number of iterations.  Nevertheless, most BO methods are sequential and perform evaluations at just one input location, at each iteration. Sometimes, however, we may evaluate several configurations in parallel. If this is the case, as when a cluster of computers is available, sequential evaluations result in a waste of resources. To avoid this, one has to choose which locations to evaluate in parallel, at each iteration. This talk introduces PPESMOC, Parallel Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints, an information-based batch method for the simultaneous optimization of multiple expensive-to-evaluate black-box functions under the presence of several constraints. Iteratively, PPESMOC selects a batch of input locations at which to evaluate the black-boxes in parallel so as to maximally reduce the entropy of the Pareto set of the optimization problem. To our knowledge, this is the first information-based batch method for constrained multi-objective BO. We present empirical evidence in the form of several optimization problems that illustrate the effectiveness of PPESMOC. Moreover, we also show in several experiments the utility of the proposed method to tune the hyper-parameters of machine learning algorithms. 

Presentation slides

Biography: Dr. Daniel Hernández-Lobato obtained a Ph.D. and an M.Phil. in Computer Science from Universidad Autónoma de Madrid, Spain, in January 2010 and June 2007, respectively. His Ph.D. thesis received the award to the best thesis on Computer Science defended during that academic year in that institution. Between November 2009 and September 2011 he worked as a post-doc researcher at Université catholique de Louvain, Belgium. There he had the opportunity to collaborate with Prof. Pierre Dupont and Prof. Bernard Lauwerys in the identification of biomarkers for the early diagnosis of arthritis. In September 2011, he moved back to Universidad Autónoma de Madrid, and since January 2014 he works there as a Lecturer of Computer Science. His research interests are mainly focused on the Bayesian approach to machine learning, including topics such as Bayesian optimization, kernel methods, Gaussian processes, and approximate Bayesian inference. He has participated, as an invited speaker, in the workshop on Gaussian process approximations, in 2015 and 2017, and in the Second workshop on Gaussian processes at Saint-Étienne, in 2018. He was also one of the two main organizers of the Machine Learning Summer School 2018, at Universidad Autónoma de Madrid.