Related papers: Parallel dynamics of fully connected Q-Ising neura…
Parameterized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the ANN can be slow and…
We consider the ferromagnetic $q$-state Potts model with zero external field in a finite volume and assume that the stochastic evolution of this system is described by a Glauber-type dynamics parametrized by the inverse temperature $\beta$.…
Thermodynamic computing exploits fluctuations and dissipation in physical systems to efficiently solve various mathematical problems. For example, it was recently shown that certain linear algebra problems can be solved thermodynamically,…
The training of neural networks is a complex, high-dimensional, non-convex and noisy optimization problem whose theoretical understanding is interesting both from an applicative perspective and for fundamental reasons. A core challenge is…
We consider model-free reinforcement learning for infinite-horizon discounted Markov Decision Processes (MDPs) with a continuous state space and unknown transition kernel, when only a single sample path under an arbitrary policy of the…
This paper develops a novel control-theoretic framework to analyze the non-asymptotic convergence of Q-learning. We show that the dynamics of asynchronous Q-learning with a constant step-size can be naturally formulated as a discrete-time…
Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…
This paper investigates the problem of synchronization for nonlinear systems. Following a Lyapunov approach, we firstly study global synchronization of nonlinear systems in canonical control form with both distributed…
We study quantum dynamics in the framework of repeated interactions between a system and a stream of identical probes. We present a coarse-grained master equation that captures the system's dynamics in the natural regime where interactions…
We study a family of diluted attractor neural networks with a finite average number of (symmetric) connections per neuron. As in finite connectivity spin glasses, their equilibrium properties are described by order parameter functions, for…
Computer assisted procedures of Lyapunov functions defined in given neighborhoods of fixed points for flows and maps are discussed. We provide a systematic methodology for constructing explicit ranges where quadratic Lyapunov functions…
We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…
Algorithms for solving \textit{nonlinear} fixed-point equations -- such as average-reward \textit{$Q$-learning} and \textit{TD-learning} -- often involve semi-norm contractions. Achieving parameter-free optimal convergence rates for these…
Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process's probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal…
The quantum dynamics of many-qubit systems is an outstanding problem that has recently driven significant advances in both numerical methods and programmable quantum processing units. In this work, we employ a comprehensive toolbox of…
Exact density profiles in the steady state of the one-dimensional fully asymmetric simple exclusion process on semi-infinite chains are obtained in the case of forward-ordered sequential dynamics by taking the thermodynamic limit in our…
Q-learning is a regression-based approach that is widely used to formalize the development of an optimal dynamic treatment strategy. Finite dimensional working models are typically used to estimate certain nuisance parameters, and…
Open quantum systems interact with their environment, leading to nonunitary dynamics. We investigate the thermodynamics of linear Open Quantum Walks (OQWs), a class of quantum walks whose dynamics is entirely driven by the environment. We…
A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/\mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival.…
We present the convergence rates of synchronous and asynchronous Q-learning for average-reward Markov decision processes, where the absence of contraction poses a fundamental challenge. Existing non-asymptotic results overcome this…