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Register a new userLocally Differentially Private (Contextual) Bandits Learning
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We study locally differentially private (LDP) bandits learning in this paper. First, we propose simple black-box reduction frameworks that can solve a large family of context-free bandits learning problems with LDP guarantee. Based on our frameworks, we can improve previous best results for private bandits learning with one-point feedback, such as private Bandits Convex Optimization, and obtain the first result for Bandits Convex Optimization (BCO) with multi-point feedback under LDP. LDP guarantee and black-box nature make our frameworks more attractive in real applications compared with previous specifically designed and relatively weaker differentially private (DP) context-free bandits algorithms. Further, we extend our $(varepsilon, delta)$-LDP algorithm to Generalized Linear Bandits, which enjoys a sub-linear regret $tilde{O}(T^{3/4}/varepsilon)$ and is conjectured to be nearly optimal. Note that given the existing $Omega(T)$ lower bound for DP contextual linear bandits (Shariff & Sheffe, 2018), our result shows a fundamental difference between LDP and DP contextual bandits learning.
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In this paper, we study Combinatorial Semi-Bandits (CSB) that is an extension of classic Multi-Armed Bandits (MAB) under Differential Privacy (DP) and stronger Local Differential Privacy (LDP) setting. Since the server receives more information from users in CSB, it usually causes additional dependence on the dimension of data, which is a notorious side-effect for privacy preserving learning. However for CSB under two common smoothness assumptions cite{kveton2015tight,chen2016combinatorial}, we show it is possible to remove this side-effect. In detail, for $B_{infty}$-bounded smooth CSB under either $varepsilon$-LDP or $varepsilon$-DP, we prove the optimal regret bound is $Theta(frac{mB^2_{infty}ln T } {Deltaepsilon^2})$ or $tilde{Theta}(frac{mB^2_{infty}ln T} { Deltaepsilon})$ respectively, where $T$ is time period, $Delta$ is the gap of rewards and $m$ is the number of base arms, by proposing novel algorithms and matching lower bounds. For $B_1$-bounded smooth CSB under $varepsilon$-DP, we also prove the optimal regret bound is $tilde{Theta}(frac{mKB^2_1ln T} {Deltaepsilon})$ with both upper bound and lower bound, where $K$ is the maximum number of feedback in each round. All above results nearly match corresponding non-private optimal rates, which imply there is no additional price for (locally) differentially private CSB in above common settings.
In this paper we study the problem of stochastic multi-armed bandits (MAB) in the (local) differential privacy (DP/LDP) model. Unlike the previous results which need to assume bounded reward distributions, here we mainly focus on the case the reward distribution of each arm only has $(1+v)$-th moment with some $vin (0, 1]$. In the first part, we study the problem in the central $epsilon$-DP model. We first provide a near-optimal result by developing a private and robust Upper Confidence Bound (UCB) algorithm. Then, we improve the result via a private and robust version of the Successive Elimination (SE) algorithm. Finally, we show that the instance-dependent regret bound of our improved algorithm is optimal by showing its lower bound. In the second part of the paper, we study the problem in the $epsilon$-LDP model. We propose an algorithm which could be seen as locally private and robust version of the SE algorithm, and show it could achieve (near) optimal rates for both instance-dependent and instance-independent regrets. All of the above results can also reveal the differences between the problem of private MAB with bounded rewards and heavy-tailed rewards. To achieve these (near) optimal rates, we develop several new hard instances and private robust estimators as byproducts, which might could be used to other related problems. Finally, experimental results also support our theoretical analysis and show the effectiveness of our algorithms.
We present differentially private efficient algorithms for learning union of polygons in the plane (which are not necessarily convex). Our algorithms achieve $(alpha,beta)$-PAC learning and $(epsilon,delta)$-differential privacy using a sample of size $tilde{O}left(frac{1}{alphaepsilon}klog dright)$, where the domain is $[d]times[d]$ and $k$ is the number of edges in the union of polygons.
Federated learning aims to protect data privacy by collaboratively learning a model without sharing private data among users. However, an adversary may still be able to infer the private training data by attacking the released model. Differential privacy provides a statistical protection against such attacks at the price of significantly degrading the accuracy or utility of the trained models. In this paper, we investigate a utility enhancement scheme based on Laplacian smoothing for differentially private federated learning (DP-Fed-LS), where the parameter aggregation with injected Gaussian noise is improved in statistical precision without losing privacy budget. Our key observation is that the aggregated gradients in federated learning often enjoy a type of smoothness, i.e. sparsity in the graph Fourier basis with polynomial decays of Fourier coefficients as frequency grows, which can be exploited by the Laplacian smoothing efficiently. Under a prescribed differential privacy budget, convergence error bounds with tight rates are provided for DP-Fed-LS with uniform subsampling of heterogeneous Non-IID data, revealing possible utility improvement of Laplacian smoothing in effective dimensionality and variance reduction, among others. Experiments over MNIST, SVHN, and Shakespeare datasets show that the proposed method can improve model accuracy with DP-guarantee and membership privacy under both uniform and Poisson subsampling mechanisms.
In this paper, we consider online learning in generalized linear contextual bandits where rewards are not immediately observed. Instead, rewards are available to the decision-maker only after some delay, which is unknown and stochastic. We study the performance of two well-known algorithms adapted to this delayed setting: one based on upper confidence bounds, and the other based on Thompson sampling. We describe modifications on how these two algorithms should be adapted to handle delays and give regret characterizations for both algorithms. Our results contribute to the broad landscape of contextual bandits literature by establishing that both algorithms can be made to be robust to delays, thereby helping clarify and reaffirm the empirical success of these two algorithms, which are widely deployed in modern recommendation engines.
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