Alkis Kalavasis
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Alkis Kalavasis has a total of 6 co-authors. Here are the top co-authors by number of shared publications:
- Andreas Galanis
University of Oxford Wolfson Building Parks Road OX1 3QD Oxford UK
1 shared publication - Anthimos Vardis Kandiros
Department of Electrical Engineering and Computer Science MIT
1 shared publication - Christos Tzamos
UW-Madison UW-Madison University of Athens
1 shared publication - Constantine Caramanis
The University of Texas at Austin
1 shared publication - Dimitris Fotakis
National Technical University of Athens Greece
1 shared publication - Vasilis Kontonis
School of Electrical and Computer Engineering National Technical University of Athens Iroon Polytechneiou 9 15780 Athens Greece
1 shared publication
Latest Publications
- Open Access
Optimizing Solution-Samplers for Combinatorial Problems: The Landscape of Policy-Gradient Methods
Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by gradient-based methods (e.g., policy gradient) to successively obtain better solution distributions. In this work we introduce a novel theoretical framework for analyzing the effectiveness of such methods. We ask whether there exist generative models that (i) are expressive enough to generate approximately optimal solutions; (ii) have a tractable, i.e, polynomial in the size of the input, number of parameters; (iii) their optimization landscape is benign in the sense that it does not contain sub-optimal stationary points. Our main contribution is a positive answer to this question. Our result holds for a broad class of combinatorial problems including Max- and Min-Cut, Max-$k$-CSP, Maximum-Weight-Bipartite-Matching, and the Traveling Salesman Problem. As a byproduct of our analysis we introduce a novel regularization process over vanilla gradient descent and provide theoretical and experimental evidence that it helps address vanishing-gradient issues and escape bad stationary points.
Open AccessOptimizing Solution-Samplers for Combinatorial Problems: The Landscape of Policy-Gradient Methods
Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by gradient-based methods (e.g., policy gradient) to successively obtain better solution distributions. In this work we introduce a novel theoretical framework for analyzing the effectiveness of such methods. We ask whether there exist generative models that (i) are expressive enough to generate approximately optimal solutions; (ii) have a tractable, i.e, polynomial in the size of the input, number of parameters; (iii) their optimization landscape is benign in the sense that it does not contain sub-optimal stationary points. Our main contribution is a positive answer to this question. Our result holds for a broad class of combinatorial problems including Max- and Min-Cut, Max-$k$-CSP, Maximum-Weight-Bipartite-Matching, and the Traveling Salesman Problem. As a byproduct of our analysis we introduce a novel regularization process over vanilla gradient descent and provide theoretical and experimental evidence that it helps address vanishing-gradient issues and escape bad stationary points.
- Open Access
Learning Hard-Constrained Models with One Sample
We consider the problem of estimating the parameters of a Markov Random Field with hard-constraints using a single sample. As our main running examples, we use the $k$-SAT and the proper coloring models, as well as general $H$-coloring models; for all of these we obtain both positive and negative results. In contrast to the soft-constrained case, we show in particular that single-sample estimation is not always possible, and that the existence of an estimator is related to the existence of non-satisfiable instances. Our algorithms are based on the pseudo-likelihood estimator. We show variance bounds for this estimator using coupling techniques inspired, in the case of $k$-SAT, by Moitra's sampling algorithm (JACM, 2019); our positive results for colorings build on this new coupling approach. For $q$-colorings on graphs with maximum degree $d$, we give a linear-time estimator when $q>d+1$, whereas the problem is non-identifiable when $q\leq d+1$. For general $H$-colorings, we show that standard conditions that guarantee sampling, such as Dobrushin's condition, are insufficient for one-sample learning; on the positive side, we provide a general condition that is sufficient to guarantee linear-time learning and obtain applications for proper colorings and permissive models. For the $k$-SAT model on formulas with maximum degree $d$, we provide a linear-time estimator when $k\gtrsim 6.45\log d$, whereas the problem becomes non-identifiable when $k\lesssim \log d$.Open AccessLearning Hard-Constrained Models with One Sample
We consider the problem of estimating the parameters of a Markov Random Field with hard-constraints using a single sample. As our main running examples, we use the $k$-SAT and the proper coloring models, as well as general $H$-coloring models; for all of these we obtain both positive and negative results. In contrast to the soft-constrained case, we show in particular that single-sample estimation is not always possible, and that the existence of an estimator is related to the existence of non-satisfiable instances. Our algorithms are based on the pseudo-likelihood estimator. We show variance bounds for this estimator using coupling techniques inspired, in the case of $k$-SAT, by Moitra's sampling algorithm (JACM, 2019); our positive results for colorings build on this new coupling approach. For $q$-colorings on graphs with maximum degree $d$, we give a linear-time estimator when $q>d+1$, whereas the problem is non-identifiable when $q\leq d+1$. For general $H$-colorings, we show that standard conditions that guarantee sampling, such as Dobrushin's condition, are insufficient for one-sample learning; on the positive side, we provide a general condition that is sufficient to guarantee linear-time learning and obtain applications for proper colorings and permissive models. For the $k$-SAT model on formulas with maximum degree $d$, we provide a linear-time estimator when $k\gtrsim 6.45\log d$, whereas the problem becomes non-identifiable when $k\lesssim \log d$.