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IEEE International Workshop on Workload Characterization (WWC)

Multi-agent stochastic control: models inspired from quantum physics

John S. Baras

Published Apr 23, 2004• 5 citations
Publisher

Abstract

In this paper, we consider multi-agent stochastic optimization and control problems, with partial information. The agent can operate in a distributed and asynchronous fashion. We investigate new problems that arise out of the interaction between observations and control actions by the agent. We show that new non-classical and non-commutative probability models are needed in order to properly formulate such problems. The models we develop here are inspired by models developed for dynamical physics problems. We establish a series of fundamental results for the trade-off between information and control patterns in distributed stochastic control, detection and estimation.

DOI
10.1109/phycon.2003.1236999

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In this paper, we consider multi-agent stochastic optimization and control problems, with partial information. The agent can operate in a distributed and asynchronous fashion. We investigate new problems that arise out of the interaction between observations and control actions by the agent. We show that new non-classical and non-commutative probability models are needed in order to properly formulate such problems. The models we develop here are inspired by models developed for dynamical physics problems. We establish a series of fundamental results for the trade-off between information and control patterns in distributed stochastic control, detection and estimation.
With multi-agent systems advancing to high-dimensional and uncertain spaces, classical learning and control methods encounter fundamental challenges related to the curse of dimensionality and limited expressivity. Quantum computing offers the potential to overcome the shortcomings by embedding data into exponentially large Hilbert spaces, capturing complex correlations. We first propose a Distributed Quantum Gaussian Process (DQGP) framework enabling agents to collaboratively learn a high-fidelity global model of the environment through improved modeling capabilities and scalability. Numerical evaluations on non-stationary NASA SRTM datasets demonstrate the enhanced predictive and uncertainty estimation performance of DQGP compared to the classical Distributed Gaussian Processes. The findings lead to the next research phase: developing a Quantum-enhanced Learning Model Predictive Control architecture that results in robust, adaptive, and scalable coordination and control of multiple agents in complex scenarios.
The paper extends the mathematical formalism of quantum physics to include games of intelligent agents that communicate due to entanglement. The novelty of the approach is based upon a human factor-based behavioral model of an intelligent agent. The model is quantum inspired: it is represented by a modified Madelung equation in which the gradient of quantum potential is replaced by a specially chosen information force. It consists of motor dynamics simulating actual behavior of the agent, and mental dynamics representing evolution of the corresponding knowledge base and incorporating this knowledge in the form of information flows into the motor dynamics. Due to feedback from mental dynamics, the motor dynamics attains quantum-like properties: its trajectory splits into a family of different trajectories, and each of those trajectories can be chosen with the probability prescribed by the mental dynamics; each agent is entangled (in a quantum way) to other agents and makes calculated predictions for future actions; human factor is associated with violation of the second law of thermodynamics: the system can move from disorder to order without external help, and that represents intrinsic intelligence. All of these departures actually extend and complement the classical methods making them especially successful in analysis of communications of agents represented by new mathematical formalism, and in particular, in agent-based economics with a human factor.
This paper explores a novel approach to distributed optimization leveraging the unique properties of quantum entanglement. Traditional distributed optimization methods often suffer from communication bottlenecks and reliance on shared information, limiting scalability and efficiency, particularly in scenarios with geographically dispersed agents. This research proposes a framework where agents collaborate to solve complex optimization problems through the utilization of quantum entanglement, effectively creating a "quantum entanglement network". The core idea is to exploit the non-local correlations inherent in entangled states for instantaneous information exchange, bypassing the need for direct communication channels. We detail a communication protocol based on entangled state manipulation and describe how an optimization algorithm can utilize this network to guide local decisions toward a global optimum. The theoretical framework demonstrates the potential for enhanced scalability and efficiency in distributed optimization, representing a significant departure from conventional approaches. The proposed method addresses the inherent limitations of classical communication in complex distributed systems, offering a fundamentally different paradigm for collaborative problem-solving. ---
In reinforcement learning, an agent interacts sequentially with an environment to maximize a reward, receiving only partial, probabilistic feedback. This creates a fundamental exploration-exploitation trade-off: the agent must explore to learn the hidden dynamics while exploiting this knowledge to maximize its target objective. While extensively studied classically, applying this framework to quantum systems requires dealing with hidden quantum states that evolve via unknown dynamics. We formalize this problem via a framework where the environment maintains a hidden quantum memory evolving via unknown quantum channels, and the agent intervenes sequentially using quantum instruments. For this setting, we adapt an optimistic maximum-likelihood estimation algorithm. We extend the analysis to continuous action spaces, allowing us to model general positive operator-valued measures (POVMs). By controlling the propagation of estimation errors through quantum channels and instruments, we prove that the cumulative regret of our strategy scales as O~(K)\widetilde{\mathcal{O}}(\sqrt{K})O(K​) over KKK episodes. Furthermore, via a reduction to the multi-armed quantum bandit problem, we establish information-theoretic lower bounds demonstrating that this sublinear scaling is strictly optimal up to polylogarithmic factors. As a physical application, we consider state-agnostic work extraction. When extracting free energy from a sequence of non-i.i.d. quantum states correlated by a hidden memory, any lack of knowledge about the source leads to thermodynamic dissipation. In our setting, the mathematical regret exactly quantifies this cumulative dissipation. Using our adaptive algorithm, the agent uses past energy outcomes to improve its extraction protocol on the fly, achieving sublinear cumulative dissipation, and, consequently, an asymptotically zero dissipation rate.
Control and manipulation of quantum mechanical systems using electromagnetic fields is a widely studied subject in areas of physics and chemistry, including spectroscopy, atomic molecular, and optical physics, and quantum chemistry.This article attempts to provide a glimpse into the rich class of bilinear control systems that are ubiquitous in these problems.In this article, we use control of spin systems in magnetic resonance as a model system to highlight characteristic feature of problems in quantum control.Background information is provided to enable the reader to appreciate new results and developments, where principled use of ideas from control theory have provided new insights into finding optimal ways to control and manipulate quantum mechanical systems.The study of deterministic and stochastic models that arise in problems in measurement and manipulation of quantum mechanical systems may foster new developments in control.
In multi-agent systems, agents observe data, and use them to make inferences and take actions. As a result sensing and control naturally interfere, more so from a real-time perspective. A natural consequence is that in multi-agent systems there are propositions based on the set of observed events that might not be simultaneously verifiable, which leads to the need for probability structures that allow such \textit{incompatible events}. We revisit the structure of events in a multi-agent system and we introduce the necessary new models that incorporate such incompatible events in the formalism. These models are essential for building non-commutative probability models, which are different than the classical models based on the Kolmogorov construction. From this perspective, we revisit the concepts of \textit{event-state-operation structure} and the needed \textit{relationship of incompatibility} from the literature and use them as a tool to study the needed new algebraic structure of the set of events. We present an example from multi-agent hypothesis testing where the set of events does not form a Boolean algebra, but forms an ortholattice. A possible construction of a `noncommutative probability space', accounting for \textit{incompatible events} is discussed. We formulate and solve the binary hypothesis testing problem in the noncommutative probability space. We illustrate the occurrence of `order effects' in the multi-agent hypothesis testing problem by computing the minimum probability of error that can be achieved with different orders of measurements.