arXiv subjects

Ruida Zhou

Publications and source records attributed to Ruida Zhou.

45 records · Page 3Linked to original sources

arXiv2021

Two-Level Private Information Retrieval

In the conventional robust $T$-colluding private information retrieval (PIR) system, the user needs to retrieve one of the possible messages while keeping the identity of the requested message private from any $T$ colluding servers. Motivated by the possible heterogeneous privacy requirements for different messages, we consider the $(N, T_1:K_1, T_2:K_2)$ two-level PIR system with a total of $K_2$ messages in the system, where $T_1\geq T_2$ and $K_1\leq K_2$. Any one of the $K_1$ messages needs to be retrieved privately against $T_1$ colluding servers, and any one of the full set of $K_2$ messages needs to be retrieved privately against $T_2$ colluding servers. We obtain a lower bound to the capacity by proposing two novel coding schemes, namely the non-uniform successive cancellation scheme and the non-uniform block cancellation scheme. A capacity upper bound is also derived. The gap between the upper bound and the lower bounds is analyzed, and shown to vanish when $T_1=T_2$. Lastly, we show that the upper bound is in general not tight by providing a stronger bound for a special setting.

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arXiv2020

Individually Conditional Individual Mutual Information Bound on Generalization Error

We propose a new information-theoretic bound on generalization error based on a combination of the error decomposition technique of Bu et al. and the conditional mutual information (CMI) construction of Steinke and Zakynthinou. In a previous work, Haghifam et al. proposed a different bound combining the two aforementioned techniques, which we refer to as the conditional individual mutual information (CIMI) bound. However, in a simple Gaussian setting, both the CMI and the CIMI bounds are order-wise worse than that by Bu et al.. This observation motivated us to propose the new bound, which overcomes this issue by reducing the conditioning terms in the conditional mutual information. In the process of establishing this bound, a conditional decoupling lemma is established, which also leads to a meaningful dichotomy and comparison among these information-theoretic bounds.

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arXiv2020

User Manual CAI version-1.0: An Open-Source Toolbox for Computer-Aided Investigation on the Fundamental Limits of Information Systems

We provide an open source toolbox on https://github.com/ct2641/CAI/releases/tag/1.0 to conduct computer-aided investigation on the fundamental limits of information systems. The toolbox relies on either Gurobi or Cplex as the linear program solving engine. The program can read a problem description file, and then fulfill the following tasks: 1) compute a bound for a given linear combination of information measures and provide the value of information measures at the optimal solution; 2) efficiently compute a polytope tradeoff outer bound between two information quantities; 3) produce a proof (as a weighted sum of known information inequalities; and 4) provide the range for information quantities between which the optimal value does not change (sensitivity analysis). This technical report provides an overview of this toolbox, a detailed description of the syntax of the problem description file, and a few example use cases.

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arXiv2020

New Results on the Storage-Retrieval Tradeoff in Private Information Retrieval Systems

In a private information retrieval (PIR) system, the user needs to retrieve one of the possible messages from a set of storage servers, but wishes to keep the identity of requested message private from any given server. Existing efforts in this area have made it clear that the efficiency of the retrieval will be impacted significantly by the amount of the storage space allowed at the servers. In this work, we consider the tradeoff between the storage cost and the retrieval cost. We first present three fundamental results: 1) a regime-wise 2-approximate characterization of the optimal tradeoff, 2) a cyclic permutation lemma that can produce more sophisticated codes from simpler ones, and 3) a relaxed entropic linear program (LP) lower bound that has a polynomial complexity. Equipped with the cyclic permutation lemma, we then propose two novel code constructions, and by applying the lemma, obtain new storage-retrieval points. Furthermore, we derive more explicit lower bounds by utilizing only a subset of the constraints in the relaxed entropic LP in a systematic manner. Though the new upper bound and lower bound do not lead to a more precise approximate characterization in general, they are significantly tighter than the existing art.

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arXiv2020

On the Information Leakage in Private Information Retrieval Systems

We consider information leakage to the user in private information retrieval (PIR) systems. Information leakage can be measured in terms of individual message leakage or total leakage. Individual message leakage, or simply individual leakage, is defined as the amount of information that the user can obtain on any individual message that is not being requested, and the total leakage is defined as the amount of information that the user can obtain about all the other messages except the one being requested. In this work, we characterize the tradeoff between the minimum download cost and the individual leakage, and that for the total leakage, respectively. New codes are proposed to achieve these optimal tradeoffs, which are also shown to be optimal in terms of the message size. We further characterize the optimal tradeoff between the minimum amount of common randomness and the total leakage. Moreover, we show that under individual leakage, common randomness is in fact unnecessary when there are more than two messages.

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arXiv2020

Capacity-Achieving Private Information Retrieval Codes from MDS-Coded Databases with Minimum Message Size

We consider constructing capacity-achieving linear codes with minimum message size for private information retrieval (PIR) from $N$ non-colluding databases, where each message is coded using maximum distance separable (MDS) codes, such that it can be recovered from accessing the contents of any $T$ databases. It is shown that the minimum message size (sometimes also referred to as the sub-packetization factor) is significantly, in fact exponentially, lower than previously believed. More precisely, when $K>T/\textbf{gcd}(N,T)$ where $K$ is the total number of messages in the system and $\textbf{gcd}(\cdot,\cdot)$ means the greatest common divisor, we establish, by providing both novel code constructions and a matching converse, the minimum message size as $\textbf{lcm}(N-T,T)$, where $\textbf{lcm}(\cdot,\cdot)$ means the least common multiple. On the other hand, when $K$ is small, we show that it is in fact possible to design codes with a message size even smaller than $\textbf{lcm}(N-T,T)$.

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arXiv2018

Cost-aware Cascading Bandits

In this paper, we propose a cost-aware cascading bandits model, a new variant of multi-armed ban- dits with cascading feedback, by considering the random cost of pulling arms. In each step, the learning agent chooses an ordered list of items and examines them sequentially, until certain stopping condition is satisfied. Our objective is then to max- imize the expected net reward in each step, i.e., the reward obtained in each step minus the total cost in- curred in examining the items, by deciding the or- dered list of items, as well as when to stop examina- tion. We study both the offline and online settings, depending on whether the state and cost statistics of the items are known beforehand. For the of- fline setting, we show that the Unit Cost Ranking with Threshold 1 (UCR-T1) policy is optimal. For the online setting, we propose a Cost-aware Cas- cading Upper Confidence Bound (CC-UCB) algo- rithm, and show that the cumulative regret scales in O(log T ). We also provide a lower bound for all α-consistent policies, which scales in Ω(log T ) and matches our upper bound. The performance of the CC-UCB algorithm is evaluated with both synthetic and real-world data.

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arXiv2018

Cost-Aware Learning and Optimization for Opportunistic Spectrum Access

In this paper, we investigate cost-aware joint learning and optimization for multi-channel opportunistic spectrum access in a cognitive radio system. We investigate a discrete time model where the time axis is partitioned into frames. Each frame consists of a sensing phase, followed by a transmission phase. During the sensing phase, the user is able to sense a subset of channels sequentially before it decides to use one of them in the following transmission phase. We assume the channel states alternate between busy and idle according to independent Bernoulli random processes from frame to frame. To capture the inherent uncertainty in channel sensing, we assume the reward of each transmission when the channel is idle is a random variable. We also associate random costs with sensing and transmission actions. Our objective is to understand how the costs and reward of the actions would affect the optimal behavior of the user in both offline and online settings, and design the corresponding opportunistic spectrum access strategies to maximize the expected cumulative net reward (i.e., reward-minus-cost). We start with an offline setting where the statistics of the channel status, costs and reward are known beforehand. We show that the the optimal policy exhibits a recursive double threshold structure, and the user needs to compare the channel statistics with those thresholds sequentially in order to decide its actions. With such insights, we then study the online setting, where the statistical information of the channels, costs and reward are unknown a priori. We judiciously balance exploration and exploitation, and show that the cumulative regret scales in O(log T). We also establish a matched lower bound, which implies that our online algorithm is order-optimal. Simulation results corroborate our theoretical analysis.

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arXiv2018

Regional Multi-Armed Bandits

We consider a variant of the classic multi-armed bandit problem where the expected reward of each arm is a function of an unknown parameter. The arms are divided into different groups, each of which has a common parameter. Therefore, when the player selects an arm at each time slot, information of other arms in the same group is also revealed. This regional bandit model naturally bridges the non-informative bandit setting where the player can only learn the chosen arm, and the global bandit model where sampling one arms reveals information of all arms. We propose an efficient algorithm, UCB-g, that solves the regional bandit problem by combining the Upper Confidence Bound (UCB) and greedy principles. Both parameter-dependent and parameter-free regret upper bounds are derived. We also establish a matching lower bound, which proves the order-optimality of UCB-g. Moreover, we propose SW-UCB-g, which is an extension of UCB-g for a non-stationary environment where the parameters slowly vary over time.

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