Aspiration-based Perturbed Learning Automata in Games with Noisy Utility Measurements. Part A: Stochastic Stability in Non-zero-Sum Games
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915636336132096 |
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| author | Chasparis, Georgios C. |
| author_facet | Chasparis, Georgios C. |
| contents | Reinforcement-based learning has attracted considerable attention both in modeling human behavior as well as in engineering, for designing measurement- or payoff-based optimization schemes. Such learning schemes exhibit several advantages, especially in relation to filtering out noisy observations. However, they may exhibit several limitations when applied in a distributed setup. In multi-player weakly-acyclic games, and when each player applies an independent copy of the learning dynamics, convergence to (usually desirable) pure Nash equilibria cannot be guaranteed. Prior work has only focused on a small class of games, namely potential and coordination games. To address this main limitation, this paper introduces a novel payoff-based learning scheme for distributed optimization, namely aspiration-based perturbed learning automata (APLA). In this class of dynamics, and contrary to standard reinforcement-based learning schemes, each player's probability distribution for selecting actions is reinforced both by repeated selection and an aspiration factor that captures the player's satisfaction level. We provide a stochastic stability analysis of APLA in multi-player positive-utility games under the presence of noisy observations. This is the first part of the paper that characterizes stochastic stability in generic non-zero-sum games by establishing equivalence of the induced infinite-dimensional Markov chain with a finite dimensional one. In the second part, stochastic stability is further specialized to weakly acyclic games. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Aspiration-based Perturbed Learning Automata in Games with Noisy Utility Measurements. Part A: Stochastic Stability in Non-zero-Sum Games Chasparis, Georgios C. Machine Learning Computer Science and Game Theory Multiagent Systems Optimization and Control Reinforcement-based learning has attracted considerable attention both in modeling human behavior as well as in engineering, for designing measurement- or payoff-based optimization schemes. Such learning schemes exhibit several advantages, especially in relation to filtering out noisy observations. However, they may exhibit several limitations when applied in a distributed setup. In multi-player weakly-acyclic games, and when each player applies an independent copy of the learning dynamics, convergence to (usually desirable) pure Nash equilibria cannot be guaranteed. Prior work has only focused on a small class of games, namely potential and coordination games. To address this main limitation, this paper introduces a novel payoff-based learning scheme for distributed optimization, namely aspiration-based perturbed learning automata (APLA). In this class of dynamics, and contrary to standard reinforcement-based learning schemes, each player's probability distribution for selecting actions is reinforced both by repeated selection and an aspiration factor that captures the player's satisfaction level. We provide a stochastic stability analysis of APLA in multi-player positive-utility games under the presence of noisy observations. This is the first part of the paper that characterizes stochastic stability in generic non-zero-sum games by establishing equivalence of the induced infinite-dimensional Markov chain with a finite dimensional one. In the second part, stochastic stability is further specialized to weakly acyclic games. |
| title | Aspiration-based Perturbed Learning Automata in Games with Noisy Utility Measurements. Part A: Stochastic Stability in Non-zero-Sum Games |
| topic | Machine Learning Computer Science and Game Theory Multiagent Systems Optimization and Control |
| url | https://arxiv.org/abs/2511.11602 |