Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally Differentially Private Reinforcement Learning for Linear Mixture
  Markov Decision Processes   Reinforcement learning (RL) algorithms can be used to provide personalized
services, which rely on users' private and sensitive data. To protect the
users' privacy, privacy-preserving RL algorithms are in demand. In this paper,
we study RL with linear function approximation and local differential privacy
(LDP) guarantees. We propose a novel $(\varepsilon, \delta)$-LDP algorithm for
learning a class of Markov decision processes (MDPs) dubbed linear mixture
MDPs, and obtains an $\tilde{\mathcal{O}}(
d^{5/4}H^{7/4}T^{3/4}\left(\log(1/\delta)\right)^{1/4}\sqrt{1/\varepsilon})$
regret, where $d$ is the dimension of feature mapping, $H$ is the length of the
planning horizon, and $T$ is the number of interactions with the environment.
We also prove a lower bound
$\Omega(dH\sqrt{T}/\left(e^{\varepsilon}(e^{\varepsilon}-1)\right))$ for
learning linear mixture MDPs under $\varepsilon$-LDP constraint. Experiments on
synthetic datasets verify the effectiveness of our algorithm. To the best of
our knowledge, this is the first provable privacy-preserving RL algorithm with
linear function approximation.

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The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio