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Improved regret bounds in tabular RL under local differential privacy — arXiv:2611.03026

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.03026
License (as archived): CC0-1.0
Archived: 2026-11-03T18:38:48.785Z
SHA-256 of the archived text: 94fd6826c6d26e284f50e07d74bec3e60ea27fd0b06519937af3e5b21b84622f
Stable URL of this page: https://metraipolis.com/documento/dc_ebddaef6eb94

How to cite

Improved regret bounds in tabular RL under local differential privacy — arXiv:2611.03026 — arXiv (en), https://arxiv.org/abs/2611.03026 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ebddaef6eb94 (Metraipolis archive dc_ebddaef6eb94, sha256 94fd6826c6d26e284f50e07d74bec3e60ea27fd0b06519937af3e5b21b84622f)

BibTeX

@misc{dcebddaef6eb94,
  title = {Improved regret bounds in tabular RL under local differential privacy — arXiv:2611.03026},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.03026},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ebddaef6eb94; sha256 94fd6826c6d26e284f50e07d74bec3e60ea27fd0b06519937af3e5b21b84622f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.03026. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study regret minimization for time-homogeneous episodic tabular reinforcement learning with $S$ states and $A$ actions under non-interactive $\epsilon$-local differential privacy (LDP). In each episode $k \in [K]$, the decision-maker sends a policy to a user, the user executes the policy for $H$ steps, and sends an $\epsilon$-locally differentially private message back to the decision-maker. When $H=1$, the problem reduces to an LDP contextual bandit with $S$ contexts, $A$ arms and horizon $K$. We prove that the minimax regret is $\min\bigg(K, \frac{ \sqrt{\max( S, \exp(\epsilon) + 1) S A K (\exp(\epsilon) + 1)}}{\exp(\epsilon) - 1}\bigg)$, up to constants and a $\sqrt{\log(A)}$ factor. The upper bound is achieved by an adaptation of EXP3 and a unary encoding mechanism. When $H > 1$, and for small $\epsilon$, we show a lower bound in $\Omega(HS\frac{\sqrt{A K}}{\epsilon})$ and an upper bound in $\tilde{O}(H^2 S^2 \frac{\sqrt{ AK}}{\epsilon})$. The upper bound is achieved by an algorithm based on UCBVI and a unary encoding mechanism. For small $\epsilon$, these bounds improve the previously known lower bound by a factor $\sqrt{S}$ and the previously known upper bound by a factor of $H \sqrt{A}$.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2611.03026 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:12:54.607Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).