The slowing down of Moore's law has driven the development of unconventional computing paradigms, such as specialized Ising machines tailored to solve combinatorial optimization problems. In this paper, we show a new application domain for probabilistic bit (p-bit) based Ising machines by training deep generative AI models with them. Using sparse, asynchronous, and massively parallel Ising machines we train deep Boltzmann networks in a hybrid probabilistic-classical computing setup. We use the full MNIST dataset without any downsampling or reduction in hardware-aware network topologies implemented in moderately sized Field Programmable Gate Arrays (FPGA). Our machine, which uses only 4,264 nodes (p-bits) and about 30,000 parameters, achieves the same classification accuracy (90%) as an optimized software-based restricted Boltzmann Machine (RBM) with approximately 3.25 million parameters. Additionally, the sparse deep Boltzmann network can generate new handwritten digits, a task the 3.25 million parameter RBM fails at despite achieving the same accuracy. Our hybrid computer takes a measured 50 to 64 billion probabilistic flips per second, which is at least an order of magnitude faster than superficially similar Graphics and Tensor Processing Unit (GPU/TPU) based implementations. The massively parallel architecture can comfortably perform the contrastive divergence algorithm (CD-n) with up to n = 10 million sweeps per update, beyond the capabilities of existing software implementations. These results demonstrate the potential of using Ising machines for traditionally hard-to-train deep generative Boltzmann networks, with further possible improvement in nanodevice-based realizations.

Recently, mean field control (MFC) has provided a tractable and theoretically founded approach to otherwise difficult cooperative multi-agent control. However, the strict assumption of many independent, homogeneous agents may be too stringent in practice. In this work, we propose a novel discrete-time generalization of Markov decision processes and MFC to both many minor agents and potentially complex major agents -- major-minor mean field control (M3FC). In contrast to deterministic MFC, M3FC allows for stochastic minor agent distributions with strong correlation between minor agents through the major agent state, which can model arbitrary problem details not bound to any agent. Theoretically, we give rigorous approximation properties with novel proofs for both M3FC and existing MFC models in the finite multi-agent problem, together with a dynamic programming principle for solving such problems. In the infinite-horizon discounted case, existence of an optimal stationary policy follows. Algorithmically, we propose the major-minor mean field proximal policy optimization algorithm (M3FPPO) as a novel multi-agent reinforcement learning algorithm and demonstrate its success in illustrative M3FC-type problems.

The Variational Monte Carlo (VMC) is a promising approach for computing the ground state energy of many-body quantum problems and attracts more and more interests due to the development of machine learning. The recent paradigms in VMC construct neural networks as trial wave functions, sample quantum configurations using Markov chain Monte Carlo (MCMC) and train neural networks with stochastic gradient descent (SGD) method. However, the theoretical convergence of VMC is still unknown when SGD interacts with MCMC sampling given a well-designed trial wave function. Since MCMC reduces the difficulty of estimating gradients, it has inevitable bias in practice. Moreover, the local energy may be unbounded, which makes it harder to analyze the error of MCMC sampling. Therefore, we assume that the local energy is sub-exponential and use the Bernstein inequality for non-stationary Markov chains to derive error bounds of the MCMC estimator. Consequently, VMC is proven to have a first order convergence rate $O(\log K/\sqrt{n K})$ with $K$ iterations and a sample size $n$. It partially explains how MCMC influences the behavior of SGD. Furthermore, we verify the so-called correlated negative curvature condition and relate it to the zero-variance phenomena in solving eigenvalue functions. It is shown that VMC escapes from saddle points and reaches $(\epsilon,\epsilon^{1/4})$ -approximate second order stationary points or $\epsilon^{1/2}$-variance points in at least $O(\epsilon^{-11/2}\log^{2}(1/\epsilon) )$ steps with high probability. Our analysis enriches the understanding of how VMC converges efficiently and can be applied to general variational methods in physics and statistics.

In reinforcement learning, the classic objectives of maximizing discounted and finite-horizon cumulative rewards are PAC-learnable: There are algorithms that learn a near-optimal policy with high probability using a finite amount of samples and computation. In recent years, researchers have introduced objectives and corresponding reinforcement-learning algorithms beyond the classic cumulative rewards, such as objectives specified as linear temporal logic formulas. However, questions about the PAC-learnability of these new objectives have remained open. This work demonstrates the PAC-learnability of general reinforcement-learning objectives through sufficient conditions for PAC-learnability in two analysis settings. In particular, for the analysis that considers only sample complexity, we prove that if an objective given as an oracle is uniformly continuous, then it is PAC-learnable. Further, for the analysis that considers computational complexity, we prove that if an objective is computable, then it is PAC-learnable. In other words, if a procedure computes successive approximations of the objective's value, then the objective is PAC-learnable. We give three applications of our condition on objectives from the literature with previously unknown PAC-learnability and prove that these objectives are PAC-learnable. Overall, our result helps verify existing objectives' PAC-learnability. Also, as some studied objectives that are not uniformly continuous have been shown to be not PAC-learnable, our results could guide the design of new PAC-learnable objectives.

The interaction and collaboration between humans and multiple robots represent a novel field of research known as human multi-robot systems. Adequately designed systems within this field allow teams composed of both humans and robots to work together effectively on tasks such as monitoring, exploration, and search and rescue operations. This paper presents a deep reinforcement learning-based affective workload allocation controller specifically for multi-human multi-robot teams. The proposed controller can dynamically reallocate workloads based on the performance of the operators during collaborative missions with multi-robot systems. The operators' performances are evaluated through the scores of a self-reported questionnaire (i.e., subjective measurement) and the results of a deep learning-based cognitive workload prediction algorithm that uses physiological and behavioral data (i.e., objective measurement). To evaluate the effectiveness of the proposed controller, we use a multi-human multi-robot CCTV monitoring task as an example and carry out comprehensive real-world experiments with 32 human subjects for both quantitative measurement and qualitative analysis. Our results demonstrate the performance and effectiveness of the proposed controller and highlight the importance of incorporating both subjective and objective measurements of the operators' cognitive workload as well as seeking consent for workload transitions, to enhance the performance of multi-human multi-robot teams.

Stochastic optimal control and games have found a wide range of applications, from finance and economics to social sciences, robotics and energy management. Many real-world applications involve complex models which have driven the development of sophisticated numerical methods. Recently, computational methods based on machine learning have been developed for stochastic control problems and games. We review such methods, with a focus on deep learning algorithms that have unlocked the possibility to solve such problems even when the dimension is high or when the structure is very complex, beyond what is feasible with traditional numerical methods. Here, we consider mostly the continuous time and continuous space setting. Many of the new approaches build on recent neural-network based methods for high-dimensional partial differential equations or backward stochastic differential equations, or on model-free reinforcement learning for Markov decision processes that have led to breakthrough results. In this paper we provide an introduction to these methods and summarize state-of-the-art works on machine learning for stochastic control and games.

We study reward-free reinforcement learning (RL) with linear function approximation, where the agent works in two phases: (1) in the exploration phase, the agent interacts with the environment but cannot access the reward; and (2) in the planning phase, the agent is given a reward function and is expected to find a near-optimal policy based on samples collected in the exploration phase. The sample complexities of existing reward-free algorithms have a polynomial dependence on the planning horizon, which makes them intractable for long planning horizon RL problems. In this paper, we propose a new reward-free algorithm for learning linear mixture Markov decision processes (MDPs), where the transition probability can be parameterized as a linear combination of known feature mappings. At the core of our algorithm is uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward and a high-order moment estimator for the aleatoric and epistemic uncertainties. When the total reward is bounded by $1$, we show that our algorithm only needs to explore $\tilde O( d^2\varepsilon^{-2})$ episodes to find an $\varepsilon$-optimal policy, where $d$ is the dimension of the feature mapping. The sample complexity of our algorithm only has a polylogarithmic dependence on the planning horizon and therefore is ``horizon-free''. In addition, we provide an $\Omega(d^2\varepsilon^{-2})$ sample complexity lower bound, which matches the sample complexity of our algorithm up to logarithmic factors, suggesting that our algorithm is optimal.

We introduce a new optimization algorithm, termed contrastive adjustment, for learning Markov transition kernels whose stationary distribution matches the data distribution. Contrastive adjustment is not restricted to a particular family of transition distributions and can be used to model data in both continuous and discrete state spaces. Inspired by recent work on noise-annealed sampling, we propose a particular transition operator, the noise kernel, that can trade mixing speed for sample fidelity. We show that contrastive adjustment is highly valuable in humancomputer design processes, as the stationarity of the learned Markov chain enables local exploration of the data manifold and makes it possible to iteratively refine outputs by human feedback. We compare the performance of noise kernels trained with contrastive adjustment to current state-of-the-art generative models and demonstrate promising results on a variety of image synthesis tasks. Figure 1: Unconditional samples from noise kernels trained with contrastive adjustment.

We study learning in periodic Markov Decision Process (MDP), a special type of non-stationary MDP where both the state transition probabilities and reward functions vary periodically, under the average reward maximization setting. We formulate the problem as a stationary MDP by augmenting the state space with the period index, and propose a periodic upper confidence bound reinforcement learning-2 (PUCRL2) algorithm. We show that the regret of PUCRL2 varies linearly with the period $N$ and as $\mathcal{O}(\sqrt{Tlog T})$ with the horizon length $T$. Utilizing the information about the sparsity of transition matrix of augmented MDP, we propose another algorithm PUCRLB which enhances upon PUCRL2, both in terms of regret ($O(\sqrt{N})$ dependency on period) and empirical performance. Finally, we propose two other algorithms U-PUCRL2 and U-PUCRLB for extended uncertainty in the environment in which the period is unknown but a set of candidate periods are known. Numerical results demonstrate the efficacy of all the algorithms.

Prescriptive Process Monitoring is a prominent problem in Process Mining, which consists in identifying a set of actions to be recommended with the goal of optimising a target measure of interest or Key Performance Indicator (KPI). One challenge that makes this problem difficult is the need to provide Prescriptive Process Monitoring techniques only based on temporally annotated (process) execution data, stored in, so-called execution logs, due to the lack of well crafted and human validated explicit models. In this paper we aim at proposing an AI based approach that learns, by means of Reinforcement Learning (RL), an optimal policy (almost) only from the observation of past executions and recommends the best activities to carry on for optimizing a KPI of interest. This is achieved first by learning a Markov Decision Process for the specific KPIs from data, and then by using RL training to learn the optimal policy. The approach is validated on real and synthetic datasets and compared with off-policy Deep RL approaches. The ability of our approach to compare with, and often overcome, Deep RL approaches provides a contribution towards the exploitation of white box RL techniques in scenarios where only temporal execution data are available.