Our code is in python (+ pytorch) and will be made available in Github.

This problem-dependent sample complexity result is expressed in terms of the sub-optimality gaps of the state-action pairs that are visited during exploration.

This problem-dependent sample complexity result is expressed in terms of the sub-optimality gaps of the state-action pairs that are visited during exploration.

Submodular and supermodular functions have found wide applicability in machine learning, capturing notions such as diversity and regularity, respectively. These notions have deep consequences for optimization, and the problem of (approximately) optimizing submodular functions has received much attention. However, beyond optimization, these notions allow specifying expressive probabilistic models that can be used to quantify predictive uncertainty via marginal inference. Prominent, well-studied special cases include Ising models and determinan-tal point processes, but the general class of log-submodular and log-supermodular models is much richer and little studied. In this paper, we investigate the use of Markov chain Monte Carlo sampling to perform approximate inference in general log-submodular and log-supermodular models. In particular, we consider a simple Gibbs sampling procedure, and establish two sufficient conditions, the first guaranteeing polynomial-time, and the second fast ( O ( n log n)) mixing. We also evaluate the efficiency of the Gibbs sampler on three examples of such models, and compare against a recently proposed variational approach.

Restricted Boltzmann machines are undirected neural networks which have been shown to be effective in many applications, including serving as initializations for training deep multi-layer neural networks. One of the main reasons for their success is the existence of efficient and practical stochastic algorithms, such as contrastive divergence, for unsupervised training. We propose an alternative deterministic iterative procedure based on an improved mean field method from statistical physics known as the Thouless-Anderson-Palmer approach. We demonstrate that our algorithm provides performance equal to, and sometimes superior to, persistent contrastive divergence, while also providing a clear and easy to evaluate objective function. We believe that this strategy can be easily generalized to other models as well as to more accurate higher-order approximations, paving the way for systematic improvements in training Boltzmann machines with hidden units.

By making personalized suggestions, a recommender system is playing a crucial role in improving the engagement of users in modern web-services. However, most recommendation algorithms do not explicitly take into account the temporal behavior and the recurrent activities of users. Two central but less explored questions are how to recommend the most desirable item at the right moment, and how to predict the next returning time of a user to a service. To address these questions, we propose a novel framework which connects self-exciting point processes and low-rank models to capture the recurrent temporal patterns in a large collection of user-item consumption pairs. We show that the parameters of the model can be estimated via a convex optimization, and furthermore, we develop an efficient algorithm that maintains O (1 /null) convergence rate, scales up to problems with millions of user-item pairs and hundreds of millions of temporal events. Compared to other state-of-the-arts in both synthetic and real datasets, our model achieves superb predictive performance in the two time-sensitive recommendation tasks. Finally, we point out that our formulation can incorporate other extra context information of users, such as profile, textual and spatial features.

Neural Information Processing Systems http://nips.cc/

State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states

Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of marginals. However, existing approaches for learning parameters of PTNs are either computationally demanding and not fully compatible with automatic differentiation frameworks, or numerically unstable. In this work, we propose a conceptually simple approach for learning PTNs efficiently, that is numerically stable. We show our method provides significant improvements in time and space complexity, achieving 10x reduction in latency for generative modeling on the MNIST dataset. Furthermore, our approach enables learning of distributions with 10x more variables than previous approaches when applied to a variety of density estimation benchmarks. Our code is publicly available at github.com/marawangamal/ptn.

Reinforcement learning (RL) struggles to scale to large, combinatorial action spaces common in many real-world problems. This paper introduces a novel framework for training discrete diffusion models as highly effective policies in these complex settings. Our key innovation is an efficient online training process that ensures stable and effective policy improvement. By leveraging policy mirror descent (PMD) to define an ideal, regularized target policy distribution, we frame the policy update as a distributional matching problem, training the expressive diffusion model to replicate this stable target. This decoupled approach stabilizes learning and significantly enhances training performance. Our method achieves state-of-the-art results and superior sample efficiency across a diverse set of challenging combinatorial benchmarks, including DNA sequence generation, RL with macro-actions, and multi-agent systems. Experiments demonstrate that our diffusion policies attain superior performance compared to other baselines.