We propose in this paper, STANLEY, a STochastic gradient ANisotropic LangEvin dYnamics, for sampling high dimensional data. With the growing efficacy and potential of Energy-Based modeling, also known as non-normalized probabilistic modeling, for modeling a generative process of different natures of high dimensional data observations, we present an end-to-end learning algorithm for Energy-Based models (EBM) with the purpose of improving the quality of the resulting sampled data points. While the unknown normalizing constant of EBMs makes the training procedure intractable, resorting to Markov Chain Monte Carlo (MCMC) is in general a viable option. Realizing what MCMC entails for the EBM training, we propose in this paper, a novel high dimensional sampling method, based on an anisotropic stepsize and a gradient-informed covariance matrix, embedded into a discretized Langevin diffusion. We motivate the necessity for an anisotropic update of the negative samples in the Markov Chain by the nonlinearity of the backbone of the EBM, here a Convolutional Neural Network. Our resulting method, namely STANLEY, is an optimization algorithm for training Energy-Based models via our newly introduced MCMC method. We provide a theoretical understanding of our sampling scheme by proving that the sampler leads to a geometrically uniformly ergodic Markov Chain. Several image generation experiments are provided in our paper to show the effectiveness of our method.

Inference on modern Bayesian Neural Networks (BNNs) often relies on a variational inference treatment, imposing violated assumptions of independence and the form of the posterior. Traditional MCMC approaches avoid these assumptions at the cost of increased computation due to its incompatibility to subsampling of the likelihood. New Piecewise Deterministic Markov Process (PDMP) samplers permit subsampling, though introduce a model specific inhomogenous Poisson Process (IPPs) which is difficult to sample from. This work introduces a new generic and adaptive thinning scheme for sampling from these IPPs, and demonstrates how this approach can accelerate the application of PDMPs for inference in BNNs. Experimentation illustrates how inference with these methods is computationally feasible, can improve predictive accuracy, MCMC mixing performance, and provide informative uncertainty measurements when compared against other approximate inference schemes.

A metric tensor for Riemann manifold Monte Carlo particularly suited for non-linear Bayesian hierarchical models is proposed. The metric tensor is built from symmetric positive semidefinite log-density gradient covariance (LGC) matrices, which are also proposed and further explored here. The LGCs generalize the Fisher information matrix by measuring the joint information content and dependence structure of both a random variable and the parameters of said variable. Consequently, positive definite Fisher/LGC-based metric tensors may be constructed not only from the observation likelihoods as is current practice, but also from arbitrarily complicated non-linear prior/latent variable structures, provided the LGC may be derived for each conditional distribution used to construct said structures. The proposed methodology is highly automatic and allows for exploitation of any sparsity associated with the model in question. When implemented in conjunction with a Riemann manifold variant of the recently proposed numerical generalized randomized Hamiltonian Monte Carlo processes, the proposed methodology is highly competitive, in particular for the more challenging target distributions associated with Bayesian hierarchical models.

Partially observable Markov decision processes (POMDPs) provide a flexible representation for real-world decision and control problems. However, POMDPs are notoriously difficult to solve, especially when the state and observation spaces are continuous or hybrid, which is often the case for physical systems. While recent online sampling-based POMDP algorithms that plan with observation likelihood weighting have shown practical effectiveness, a general theory characterizing the approximation error of the particle filtering techniques that these algorithms use has not previously been proposed. Our main contribution is bounding the error between any POMDP and its corresponding finite sample particle belief MDP (PB-MDP) approximation. This fundamental bridge between PB-MDPs and POMDPs allows us to adapt any sampling-based MDP algorithm to a POMDP by solving the corresponding particle belief MDP, thereby extending the convergence guarantees of the MDP algorithm to the POMDP. Practically, this is implemented by using the particle filter belief transition model as the generative model for the MDP solver. While this requires access to the observation density model from the POMDP, it only increases the transition sampling complexity of the MDP solver by a factor of $\mathcal{O}(C)$, where $C$ is the number of particles. Thus, when combined with sparse sampling MDP algorithms, this approach can yield algorithms for POMDPs that have no direct theoretical dependence on the size of the state and observation spaces. In addition to our theoretical contribution, we perform five numerical experiments on benchmark POMDPs to demonstrate that a simple MDP algorithm adapted using PB-MDP approximation, Sparse-PFT, achieves performance competitive with other leading continuous observation POMDP solvers.

This paper studies a long-term resource allocation problem over multiple periods where each period requires a multi-stage decision-making process. We formulate the problem as an online allocation problem in an episodic finite-horizon constrained Markov decision process with an unknown non-stationary transition function and stochastic non-stationary reward and resource consumption functions. We propose the observe-then-decide regime and improve the existing decide-then-observe regime, while the two settings differ in how the observations and feedback about the reward and resource consumption functions are given to the decision-maker. We develop an online dual mirror descent algorithm that achieves near-optimal regret bounds for both settings. For the observe-then-decide regime, we prove that the expected regret against the dynamic clairvoyant optimal policy is bounded by $\tilde O(\rho^{-1}{H^{3/2}}S\sqrt{AT})$ where $\rho\in(0,1)$ is the budget parameter, $H$ is the length of the horizon, $S$ and $A$ are the numbers of states and actions, and $T$ is the number of episodes. For the decide-then-observe regime, we show that the regret against the static optimal policy that has access to the mean reward and mean resource consumption functions is bounded by $\tilde O(\rho^{-1}{H^{3/2}}S\sqrt{AT})$ with high probability. We test the numerical efficiency of our method for a variant of the resource-constrained inventory management problem.

Stochastic games are a well established model for multi-agent sequential decision making under uncertainty. In reality, though, agents have only partial observability of their environment, which makes the problem computationally challenging, even in the single-agent setting of partially observable Markov decision processes. Furthermore, in practice, agents increasingly perceive their environment using data-driven approaches such as neural networks trained on continuous data. To tackle this problem, we propose the model of neuro-symbolic partially-observable stochastic games (NS-POSGs), a variant of continuous-space concurrent stochastic games that explicitly incorporates perception mechanisms. We focus on a one-sided setting, comprising a partially-informed agent with discrete, data-driven observations and a fully-informed agent with continuous observations. We present a new point-based method, called one-sided NS-HSVI, for approximating values of one-sided NS-POSGs and implement it based on the popular particle-based beliefs, showing that it has closed forms for computing values of interest. We provide experimental results to demonstrate the practical applicability of our method for neural networks whose preimage is in polyhedral form.

Imitation learning is a powerful tool for training robot manipulation policies, allowing them to learn from expert demonstrations without manual programming or trial-and-error. However, common methods of data collection, such as human supervision, scale poorly, as they are time-consuming and labor-intensive. In contrast, Task and Motion Planning (TAMP) can autonomously generate large-scale datasets of diverse demonstrations. In this work, we show that the combination of large-scale datasets generated by TAMP supervisors and flexible Transformer models to fit them is a powerful paradigm for robot manipulation. To that end, we present a novel imitation learning system called OPTIMUS that trains large-scale visuomotor Transformer policies by imitating a TAMP agent. OPTIMUS introduces a pipeline for generating TAMP data that is specifically curated for imitation learning and can be used to train performant transformer-based policies. In this paper, we present a thorough study of the design decisions required to imitate TAMP and demonstrate that OPTIMUS can solve a wide variety of challenging vision-based manipulation tasks with over 70 different objects, ranging from long-horizon pick-and-place tasks, to shelf and articulated object manipulation, achieving 70 to 80% success rates. Video results and code at https://mihdalal.github.io/optimus/

The availability of challenging benchmarks has played a key role in the recent progress of machine learning. In cooperative multi-agent reinforcement learning, the StarCraft Multi-Agent Challenge (SMAC) has become a popular testbed for centralised training with decentralised execution. However, after years of sustained improvement on SMAC, algorithms now achieve near-perfect performance. In this work, we conduct new analysis demonstrating that SMAC lacks the stochasticity and partial observability to require complex *closed-loop* policies. In particular, we show that an *open-loop* policy conditioned only on the timestep can achieve non-trivial win rates for many SMAC scenarios. To address this limitation, we introduce SMACv2, a new version of the benchmark where scenarios are procedurally generated and require agents to generalise to previously unseen settings (from the same distribution) during evaluation. We also introduce the extended partial observability challenge (EPO), which augments SMACv2 to ensure meaningful partial observability. We show that these changes ensure the benchmark requires the use of *closed-loop* policies. We evaluate state-of-the-art algorithms on SMACv2 and show that it presents significant challenges not present in the original benchmark. Our analysis illustrates that SMACv2 addresses the discovered deficiencies of SMAC and can help benchmark the next generation of MARL methods. Videos of training are available at https://sites.google.com/view/smacv2.

We study sequential decision making problems aimed at maximizing the expected total reward while satisfying a constraint on the expected total utility. We employ the natural policy gradient method to solve the discounted infinite-horizon optimal control problem for Constrained Markov Decision Processes (constrained MDPs). Specifically, we propose a new Natural Policy Gradient Primal-Dual (NPG-PD) method that updates the primal variable via natural policy gradient ascent and the dual variable via projected sub-gradient descent. Although the underlying maximization involves a nonconcave objective function and a nonconvex constraint set, under the softmax policy parametrization we prove that our method achieves global convergence with sublinear rates regarding both the optimality gap and the constraint violation. Such convergence is independent of the size of the state-action space, i.e., it is dimension-free. Furthermore, for log-linear and general smooth policy parametrizations, we establish sublinear convergence rates up to a function approximation error caused by restricted policy parametrization. We also provide convergence and finitesample complexity guarantees for two sample-based NPG-PD algorithms. Finally, we use computational experiments to showcase the merits and the effectiveness of our approach. Keywords: Constrained Markov decision processes; Natural policy gradient; Constrained nonconvex optimization; Method of Lagrange multipliers; Primal-dual algorithms.

We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret performance compared to existing approaches. The first algorithm, although computationally inefficient, ensures a regret of $\widetilde{\mathcal{O}}\left(\sqrt{K}\right)$, where $K$ is the number of episodes. This is the first result with the optimal $K$ dependence in the considered setting. The second algorithm, which is based on the policy optimization framework, guarantees a regret of $\widetilde{\mathcal{O}}\left(K^{\frac{3}{4}} \right)$ and is computationally efficient. Both our results significantly improve over the state-of-the-art: a computationally inefficient algorithm by Kong et al. [2023] with $\widetilde{\mathcal{O}}\left(K^{\frac{4}{5}}+poly\left(\frac{1}{\lambda_{\min}}\right) \right)$ regret, for some problem-dependent constant $\lambda_{\min}$ that can be arbitrarily close to zero, and a computationally efficient algorithm by Sherman et al. [2023b] with $\widetilde{\mathcal{O}}\left(K^{\frac{6}{7}} \right)$ regret.