More Like this

1. Reinforcement Learning for Adaptive Periodic Linear Quadratic Control

   Bo Pang, Zhong-Ping Jiang (December 2019, 2019 IEEE 58th Conference on Decision and Control (CDC))

   This paper presents a first solution to the problem of adaptive LQR for continuous-time linear periodic systems. Specifically, reinforcement learning and adaptive dynamic programming (ADP) techniques are used to develop two algorithms to obtain near-optimal controllers. Firstly, the policy iteration (PI) and value iteration (VI) methods are proposed when the model is known. Then, PI-based and VI-based off-policy ADP algorithms are derived to find near-optimal solutions directly from input/state data collected along the system trajectories, without the exact knowledge of system dynamics. The effectiveness of the derived algorithms is validated using the well-known lossy Mathieu equation. 

   more » « less
2. Dynamics of Coordinate Ascent Variational Inference: A Case Study in 2D Ising Models

   https://doi.org/10.3390/e22111263  

   Plummer, Sean; Pati, Debdeep; Bhattacharya, Anirban (November 2020, Entropy)

   null (Ed.)

   Variational algorithms have gained prominence over the past two decades as a scalable computational environment for Bayesian inference. In this article, we explore tools from the dynamical systems literature to study the convergence of coordinate ascent algorithms for mean field variational inference. Focusing on the Ising model defined on two nodes, we fully characterize the dynamics of the sequential coordinate ascent algorithm and its parallel version. We observe that in the regime where the objective function is convex, both the algorithms are stable and exhibit convergence to the unique fixed point. Our analyses reveal interesting discordances between these two versions of the algorithm in the region when the objective function is non-convex. In fact, the parallel version exhibits a periodic oscillatory behavior which is absent in the sequential version. Drawing intuition from the Markov chain Monte Carlo literature, we empirically show that a parameter expansion of the Ising model, popularly called the Edward–Sokal coupling, leads to an enlargement of the regime of convergence to the global optima. 

   more » « less
3. Effective Monte Carlo Variational Inference for Binary-Variable Probabilistic Programs

   Ji, Geng; Sudderth, Erik B. (October 2020, International Conference on Probabilistic Programming)

   We propose a broadly applicable variational inference algorithm for probabilistic models with binary latent variables, using sampling to approximate expectations required for coordinate ascent updates. Applied to three real-world models for text and image and network data, our approach converges much faster than REINFORCE-style stochastic gradient algorithms, and requires fewer Monte Carlo samples. Compared to hand-crafted variational bounds with model-dependent auxiliary variables, our approach leads to tighter likelihood bounds and greater robustness to local optima. Our method is designed to integrate easily with probabilistic programming languages for effective, scalable, black-box variational inference. 

   more » « less
4. Marginalized Stochastic Natural Gradients for Black-Box Variational Inference

   Ji, Geng; Sujono, Debora; Sudderth, Erik B. (July 2021, International Conference on Machine Learning)

   Meila, Marina; Zhang, Tong (Ed.)

   Black-box variational inference algorithms use stochastic sampling to analyze diverse statistical models, like those expressed in probabilistic programming languages, without model-specific derivations. While the popular score-function estimator computes unbiased gradient estimates, its variance is often unacceptably large, especially in models with discrete latent variables. We propose a stochastic natural gradient estimator that is as broadly applicable and unbiased, but improves efficiency by exploiting the curvature of the variational bound, and provably reduces variance by marginalizing discrete latent variables. Our marginalized stochastic natural gradients have intriguing connections to classic coordinate ascent variational inference, but allow parallel updates of variational parameters, and provide superior convergence guarantees relative to naive Monte Carlo approximations. We integrate our method with the probabilistic programming language Pyro and evaluate real-world models of documents, images, networks, and crowd-sourcing. Compared to score-function estimators, we require far fewer Monte Carlo samples and consistently convergence orders of magnitude faster. 

   more » « less
5. Provable Policy Gradient Methods for Average-Reward Markov Potential Games

   Cheng, Min; Zhou, Ruida; Kumar, P R; Tian, Chao (May 2024, Proceedings of the 27th International Conference on Artificial Intelligence and Statistics (AISTATS) 2024)

   We study Markov potential games under the infinite horizon average reward criterion. Most previous studies have been for discounted rewards. We prove that both algorithms based on independent policy gradient and independent natural policy gradient converge globally to a Nash equilibrium for the average reward criterion. To set the stage for gradient-based methods, we first establish that the average reward is a smooth function of policies and provide sensitivity bounds for the differential value functions, under certain conditions on ergodicity and the second largest eigenvalue of the underlying Markov decision process (MDP). We prove that three algorithms, policy gradient, proximal-Q, and natural policy gradient (NPG), converge to an ϵ-Nash equilibrium with time complexity O(1ϵ2), given a gradient/differential Q function oracle. When policy gradients have to be estimated, we propose an algorithm with ~O(1mins,aπ(a|s)δ) sample complexity to achieve δ approximation error w.r.t~the ℓ2 norm. Equipped with the estimator, we derive the first sample complexity analysis for a policy gradient ascent algorithm, featuring a sample complexity of ~O(1/ϵ5). Simulation studies are presented. 

   more » « less