Federated UCBVI: Communication-Efficient Federated Regret Minimization with Heterogeneous Agents
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arXiv
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| Format: | Preprint |
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2024
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| author | Labbi, Safwan Tiapkin, Daniil Mancini, Lorenzo Mangold, Paul Moulines, Eric |
| author_facet | Labbi, Safwan Tiapkin, Daniil Mancini, Lorenzo Mangold, Paul Moulines, Eric |
| contents | In this paper, we present the Federated Upper Confidence Bound Value Iteration algorithm ($\texttt{Fed-UCBVI}$), a novel extension of the $\texttt{UCBVI}$ algorithm (Azar et al., 2017) tailored for the federated learning framework. We prove that the regret of $\texttt{Fed-UCBVI}$ scales as $\tilde{\mathcal{O}}(\sqrt{H^3 |\mathcal{S}| |\mathcal{A}| T / M})$, with a small additional term due to heterogeneity, where $|\mathcal{S}|$ is the number of states, $|\mathcal{A}|$ is the number of actions, $H$ is the episode length, $M$ is the number of agents, and $T$ is the number of episodes. Notably, in the single-agent setting, this upper bound matches the minimax lower bound up to polylogarithmic factors, while in the multi-agent scenario, $\texttt{Fed-UCBVI}$ has linear speed-up. To conduct our analysis, we introduce a new measure of heterogeneity, which may hold independent theoretical interest. Furthermore, we show that, unlike existing federated reinforcement learning approaches, $\texttt{Fed-UCBVI}$'s communication complexity only marginally increases with the number of agents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22908 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Federated UCBVI: Communication-Efficient Federated Regret Minimization with Heterogeneous Agents Labbi, Safwan Tiapkin, Daniil Mancini, Lorenzo Mangold, Paul Moulines, Eric Machine Learning In this paper, we present the Federated Upper Confidence Bound Value Iteration algorithm ($\texttt{Fed-UCBVI}$), a novel extension of the $\texttt{UCBVI}$ algorithm (Azar et al., 2017) tailored for the federated learning framework. We prove that the regret of $\texttt{Fed-UCBVI}$ scales as $\tilde{\mathcal{O}}(\sqrt{H^3 |\mathcal{S}| |\mathcal{A}| T / M})$, with a small additional term due to heterogeneity, where $|\mathcal{S}|$ is the number of states, $|\mathcal{A}|$ is the number of actions, $H$ is the episode length, $M$ is the number of agents, and $T$ is the number of episodes. Notably, in the single-agent setting, this upper bound matches the minimax lower bound up to polylogarithmic factors, while in the multi-agent scenario, $\texttt{Fed-UCBVI}$ has linear speed-up. To conduct our analysis, we introduce a new measure of heterogeneity, which may hold independent theoretical interest. Furthermore, we show that, unlike existing federated reinforcement learning approaches, $\texttt{Fed-UCBVI}$'s communication complexity only marginally increases with the number of agents. |
| title | Federated UCBVI: Communication-Efficient Federated Regret Minimization with Heterogeneous Agents |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2410.22908 |