Second-Order Mirror Descent: Convergence in Games Beyond Averaging and Discounting
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866917816760795136 |
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| author | Gao, Bolin Pavel, Lacra |
| author_facet | Gao, Bolin Pavel, Lacra |
| contents | In this paper, we propose a second-order extension of the continuous-time game-theoretic mirror descent (MD) dynamics, referred to as MD2, which provably converges to mere (but not necessarily strict) variationally stable states (VSS) without using common auxiliary techniques such as time-averaging or discounting. We show that MD2 enjoys no-regret as well as an exponential rate of convergence towards strong VSS upon a slight modification. MD2 can also be used to derive many novel continuous-time primal-space dynamics. We then use stochastic approximation techniques to provide a convergence guarantee of discrete-time MD2 with noisy observations towards interior mere VSS. Selected simulations are provided to illustrate our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_09982 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Second-Order Mirror Descent: Convergence in Games Beyond Averaging and Discounting Gao, Bolin Pavel, Lacra Optimization and Control Computer Science and Game Theory Machine Learning Systems and Control Dynamical Systems In this paper, we propose a second-order extension of the continuous-time game-theoretic mirror descent (MD) dynamics, referred to as MD2, which provably converges to mere (but not necessarily strict) variationally stable states (VSS) without using common auxiliary techniques such as time-averaging or discounting. We show that MD2 enjoys no-regret as well as an exponential rate of convergence towards strong VSS upon a slight modification. MD2 can also be used to derive many novel continuous-time primal-space dynamics. We then use stochastic approximation techniques to provide a convergence guarantee of discrete-time MD2 with noisy observations towards interior mere VSS. Selected simulations are provided to illustrate our results. |
| title | Second-Order Mirror Descent: Convergence in Games Beyond Averaging and Discounting |
| topic | Optimization and Control Computer Science and Game Theory Machine Learning Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2111.09982 |