SearcharxivSearch

arXiv subjects

T-H. Hubert Chan

Publications and source records attributed to T-H. Hubert Chan.

At least 19 recordsLinked to original sources

Continual Learning With Participation Privacy: An Auditable Buffering-Aggregation Recipe

Modern federated and streaming learning systems often release intermediate models, so privacy must hold for the full trajectory under adaptive interaction. Motivated by participation privacy, we study single-edit neighboring user streams, where one insertion/deletion shifts all subsequent updates and defeats standard Hamming-neighbor continual-release analyses. We give an auditable modular recipe. A randomized buffering wrapper emits bins of size $[U,2U]$, reducing single-edit streams to a Hamming-style per-bin update stream with explicit backlog/delay guarantees, where $U$ is calibrated by the privacy parameters $(\varepsilon,δ)$. We then prove a certification theorem identifying when a non-adaptive Hamming-neighbor DP proof for a continual primitive lifts to adaptive inputs: the primitive must use fresh per-round randomness and have a stable one-round privacy profile under common adaptive context. Together, these ingredients yield trajectory-level $(\varepsilon,δ)$-DP for single-edit streams using standard primitives (e.g., tree prefix sums), with an explicit privacy--latency link via $U$.

cs.CR

An Efficient Streaming Algorithm for Approximating Graphlet Distributions

In recent years, the problem of computing the frequencies of the induced $k$-vertex subgraphs of a graph, or \emph{$k$-graphlets}, has become central. One approach for this problem is to sample $k$-graphlets randomly. Classic algorithms for $k$-graphlet sampling require loading the entire graph into main memory, making them impractical for massive graphs. To bypass this limitation, Bourreau et al. (NeurIPS 2024) introduced a \emph{streaming} algorithm that through nontrivial techniques makes only $O(\log n)$ passes using $O(n \log n)$ memory. In this work we break their $O(\log n)$-pass bound by giving an algorithm that, for any fixed $c>0$, makes $O(1/c)$ passes using $\tilde O(n^{1+c})$ memory. As a consequence of their lower bound, our algorithm is optimal up to a factor of $\tilde{O}(n^c)$ in the memory usage. We use this sampling algorithm to obtain an efficient method of approximating $k$-graphlet distributions. Experiments on real-world and synthetic graphs show that our algorithm is always at least as good as the one of Bourreau et al., and outperforms it by orders of magnitude on mildly dense graphs.

cs.DS

Universal Closest Refinement on Measurable Bipartite Relations

We study the universal closest refinement problem on measurable bipartite relations over standard Borel spaces. Given prescribed side measures, the feasible class consists of finite refinement plans concentrated on the relation and carrying one fixed marginal. The main question is whether this highly nonunique class nevertheless contains a mathematically distinguished class of refinements. We show that the correct one-sided extremal criterion is level-optimal maximin, a levelwise maximin principle formulated through truncation and overflow profiles. We then prove that this structure is exactly the one selected by convex refinement: every minimizer of a strictly convex refinement criterion is level-optimal maximin, while every level-optimal maximin refinement minimizes the full class of relevant proper lower semicontinuous convex divergence functionals. Proportional response then identifies the opposite-side partner and yields a universally closest refinement pair. Our main theorem shows that every such pair is universally closest among all feasible pairs for every divergence satisfying the data-processing inequality under measurable post-processing, and conversely that every universally closest pair has this structure. We also prove a converse paired characterization for strictly convex closest pairs. Finally, we give an equilibrium-theoretic characterization of level-optimal maximin pairs through a naturally associated continuum economy with measure-valued commodities. The measure-theoretic theory requires new tools beyond the finite case, including disintegration, measurable selection, measurable max-flow/min-cut duality, augmentation arguments, and a symmetric density decomposition separating absolutely continuous and singular components.

math.FA

Mechanism Design for Automated Market Makers

Blockchains have popularized automated market makers (AMMs). An AMM exchange is an application running on a blockchain which maintains a pool of crypto-assets and automatically trades assets with users governed by some pricing function that prices the assets based on their relative demand/supply. AMMs have created an important challenge commonly known as the Miner Extractable Value (MEV). In particular, the miners who control the contents and ordering of transactions in a block can extract value by front-running and back-running users' transactions, leading to arbitrage opportunities that guarantee them risk-free returns. In this paper, we consider how to design AMM mechanisms that eliminate MEV opportunities. Specifically, we propose a new AMM mechanism that processes all transactions contained within a block in a batch. We show that our new mechanism satisfies two tiers of guarantees. First, for legacy blockchains where each block is proposed by a single (possibly rotating) miner, we prove that our mechanism satisfies arbitrage resilience, i.e., a miner cannot gain risk-free profit. Moreover, we also guarantee fair treatment among all transactions within the same block, such that the miner is unable to sell off favorable positions in the block to users or arbitragers. Second, for blockchains where the block proposal process is decentralized and offers sequencing-fairness, we prove a stronger notion called incentive compatibility -- roughly speaking, we guarantee that any individual user's best response is to follow the honest strategy.

cs.GT

Density Decomposition in Dual-Modular Optimization: Markets, Fairness, and Contracts

We study a unified framework for optimization problems defined on dual-modular instances, where the input comprises a finite ground set $V$ and two set functions: a monotone supermodular reward function $\f$ and a strictly monotone submodular cost function $\g$. This abstraction captures and generalizes classical models in economics and combinatorial optimization, including submodular utility allocation (SUA) markets and combinatorial contracts. At the core of our framework is the notion of density decomposition, which extends classical results to the dual-modular setting and uncovers structural insights into fairness and optimality. We show that the density decomposition yields a canonical vector of reward-to-cost ratios (densities) that simultaneously characterizes market equilibria, fair allocations -- via both lexicographic optimality and local maximin conditions -- and best-response strategies in contract design. Our main result proves the equivalence of these fairness notions and guarantees the existence of allocations that realize the decomposition densities. Our technical contributions include the analysis of a broad family of convex programs -- parameterized by divergences such as quadratic, logarithmic, and hockey-stick functions -- whose minimizers recover the density decomposition. We prove that any strictly convex divergence yields the same canonical density vector, and that locally maximin allocations act as universal minimizers for all divergences satisfying the data processing inequality. As an application of our framework, we determine the structure and number of critical values in the combinatorial contracts problem. Additionally, we generalize a Frank-Wolfe-type iterative method for approximating the dual-modular density decomposition, establishing both convergence guarantees and practical potential through efficient gradient oracle design.

cs.DM

Game-Theoretically Secure Distributed Protocols for Fair Allocation in Coalitional Games

We consider game-theoretically secure distributed protocols for coalition games that approximate the Shapley value with small multiplicative error. Since all known existing approximation algorithms for the Shapley value are randomized, it is a challenge to design efficient distributed protocols among mutually distrusted players when there is no central authority to generate unbiased randomness. The game-theoretic notion of maximin security has been proposed to offer guarantees to an honest player's reward even if all other players are susceptible to an adversary. Permutation sampling is often used in approximation algorithms for the Shapley value. A previous work in 1994 by Zlotkin et al. proposed a simple constant-round distributed permutation generation protocol based on commitment scheme, but it is vulnerable to rushing attacks. The protocol, however, can detect such attacks. In this work, we model the limited resources of an adversary by a violation budget that determines how many times it can perform such detectable attacks. Therefore, by repeating the number of permutation samples, an honest player's reward can be guaranteed to be close to its Shapley value. We explore both high probability and expected maximin security. We obtain an upper bound on the number of permutation samples for high probability maximin security, even with an unknown violation budget. Furthermore, we establish a matching lower bound for the weaker notion of expected maximin security in specific permutation generation protocols. We have also performed experiments on both synthetic and real data to empirically verify our results.

cs.GT

Symmetric Splendor: Unraveling Universally Closest Refinements and Fisher Market Equilibrium through Density-Friendly Decomposition

We present a comprehensive framework that unifies several research areas within the context of vertex-weighted bipartite graphs, providing deeper insights and improved solutions. The fundamental solution concept for each problem involves refinement, where vertex weights on one side are distributed among incident edges. The primary objective is to identify a refinement pair with specific optimality conditions that can be verified locally. This framework connects existing and new problems that are traditionally studied in different contexts. We explore three main problems: (1) density-friendly hypergraph decomposition, (2) universally closest distribution refinements problem, and (3) symmetric Fisher Market equilibrium. Our framework presents a symmetric view of density-friendly hypergraph decomposition, wherein hyperedges and nodes play symmetric roles. This symmetric decomposition serves as a tool for deriving precise characterizations of optimal solutions for other problems and enables the application of algorithms from one problem to another.

cs.DM

Privacy Amplification by Iteration for ADMM with (Strongly) Convex Objective Functions

We examine a private ADMM variant for (strongly) convex objectives which is a primal-dual iterative method. Each iteration has a user with a private function used to update the primal variable, masked by Gaussian noise for local privacy, without directly adding noise to the dual variable. Privacy amplification by iteration explores if noises from later iterations can enhance the privacy guarantee when releasing final variables after the last iteration. Cyffers et al. [ICML 2023] explored privacy amplification by iteration for the proximal ADMM variant, where a user's entire private function is accessed and noise is added to the primal variable. In contrast, we examine a private ADMM variant requiring just one gradient access to a user's function, but both primal and dual variables must be passed between successive iterations. To apply Balle et al.'s [NeurIPS 2019] coupling framework to the gradient ADMM variant, we tackle technical challenges with novel ideas. First, we address the non-expansive mapping issue in ADMM iterations by using a customized norm. Second, because the dual variables are not masked with any noise directly, their privacy guarantees are achieved by treating two consecutive noisy ADMM iterations as a Markov operator. Our main result is that the privacy guarantee for the gradient ADMM variant can be amplified proportionally to the number of iterations. For strongly convex objective functions, this amplification exponentially increases with the number of iterations. These amplification results align with the previously studied special case of stochastic gradient descent.

cs.LG

Fully Dynamic Algorithms for Euclidean Steiner Tree

The Euclidean Steiner tree problem asks to find a min-cost metric graph that connects a given set of \emph{terminal} points $X$ in $\mathbb{R}^d$, possibly using points not in $X$ which are called Steiner points. Even though near-linear time $(1 + ε)$-approximation was obtained in the offline setting in seminal works of Arora and Mitchell, efficient dynamic algorithms for Steiner tree is still open. We give the first algorithm that (implicitly) maintains a $(1 + ε)$-approximate solution which is accessed via a set of tree traversal queries, subject to point insertion and deletions, with amortized update and query time $O(\poly\log n)$ with high probability. Our approach is based on an Arora-style geometric dynamic programming, and our main technical contribution is to maintain the DP subproblems in the dynamic setting efficiently. We also need to augment the DP subproblems to support the tree traversal queries.

cs.CG

Game-Theoretically Secure Protocols for the Ordinal Random Assignment Problem

We study game-theoretically secure protocols for the classical ordinal assignment problem (aka matching with one-sided preference), in which each player has a total preference order on items. To achieve the fairness notion of equal treatment of equals, conventionally the randomness necessary to resolve conflicts between players is assumed to be generated by some trusted authority. However, in a distributed setting, the mutually untrusted players are responsible for generating the randomness themselves. In addition to standard desirable properties such as fairness and Pareto-efficiency, we investigate the game-theoretic notion of maximin security, which guarantees that an honest player following a protocol will not be harmed even if corrupted players deviate from the protocol. Our main contribution is an impossibility result that shows no maximin secure protocol can achieve both fairness and ordinal efficiency. Specifically, this implies that the well-known probabilistic serial (PS) mechanism by Bogomolnaia and Moulin cannot be realized by any maximin secure protocol. On the other hand, we give a maximin secure protocol that achieves fairness and stability (aka ex-post Pareto-efficiency). Moreover, inspired by the PS mechanism, we show that a variant known as the OnlinePSVar (varying rates) protocol can achieve fairness, stability and uniform dominance, which means that an honest player is guaranteed to receive an item distribution that is at least as good as a uniformly random item. In some sense, this is the best one can hope for in the case when all players have the same preference order.

cs.GT

Locally Differentially Private Sparse Vector Aggregation

Vector mean estimation is a central primitive in federated analytics. In vector mean estimation, each user $i \in [n]$ holds a real-valued vector $v_i\in [-1, 1]^d$, and a server wants to estimate the mean of all $n$ vectors. Not only so, we would like to protect each individual user's privacy. In this paper, we consider the $k$-sparse version of the vector mean estimation problem, that is, suppose that each user's vector has at most $k$ non-zero coordinates in its $d$-dimensional vector, and moreover, $k \ll d$. In practice, since the universe size $d$ can be very large (e.g., the space of all possible URLs), we would like the per-user communication to be succinct, i.e., independent of or (poly-)logarithmic in the universe size. In this paper, we are the first to show matching upper- and lower-bounds for the $k$-sparse vector mean estimation problem under local differential privacy. Specifically, we construct new mechanisms that achieve asymptotically optimal error as well as succinct communication, either under user-level-LDP or event-level-LDP. We implement our algorithms and evaluate them on synthetic as well as real-world datasets. Our experiments show that we can often achieve one or two orders of magnitude reduction in error in comparison with prior works under typical choices of parameters, while incurring insignificant communication cost.

cs.CR

On the Hardness of Opinion Dynamics Optimization with $L_1$-Budget on Varying Susceptibility to Persuasion

Recently, Abebe et al. (KDD 2018) and Chan et al. (WWW 2019) have considered an opinion dynamics optimization problem that is based on a popular model for social opinion dynamics, in which each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; moreover, the agents influence one another's opinions through an iterative process. Under certain conditions, this iterative process converges to some equilibrium opinion vector. Previous works gave an efficient local search algorithm to solve the unbudgeted variant of the problem, for which the goal is to modify the resistance of any number of agents (within some given range) such that the sum of the equilibrium opinions is minimized. On the other hand, it was proved that the $L_0$-budgeted variant is NP-hard, where the $L_0$-budget is a restriction given upfront on the number of agents whose resistance may be modified. Inspired by practical situations in which the effort to modify an agent's resistance increases with the magnitude of the change, we propose the $L_1$-budgeted variant, in which the $L_1$-budget is a restriction on the sum of the magnitudes of the changes over all agents' resistance parameters. In this work, we show that the $L_1$-budgeted variant is NP-hard via a reduction from vertex cover. However, contrary to the $L_0$-budgeted variant, a very technical argument is needed to show that the optimal solution can be achieved by focusing the given $L_1$-budget on as small a number of agents as possible, as opposed to spreading the budget over a large number of agents.

cs.SI

Bucket Oblivious Sort: An Extremely Simple Oblivious Sort

We propose a conceptually simple oblivious sort and oblivious random permutation algorithms called bucket oblivious sort and bucket oblivious random permutation. Bucket oblivious sort uses $6n\log n$ time (measured by the number of memory accesses) and $2Z$ client storage with an error probability exponentially small in $Z$. The above runtime is only $3\times$ slower than a non-oblivious merge sort baseline; for $2^{30}$ elements, it is $5\times$ faster than bitonic sort, the de facto oblivious sorting algorithm in practical implementations.

cs.DS

Opinion Dynamics with Varying Susceptibility to Persuasion via Non-Convex Local Search

A long line of work in social psychology has studied variations in people's susceptibility to persuasion -- the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people's intrinsic opinions, it is also natural to consider interventions that modify people's susceptibility to persuasion. In this work, motivated by this fact we propose a new framework for social influence. Specifically, we adopt a popular model for social opinion dynamics, where each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; agents influence one another's opinions through an iterative process. Under non-trivial conditions, this iterative process converges to some equilibrium opinion vector. For the unbudgeted variant of the problem, the goal is to select the resistance of each agent (from some given range) such that the sum of the equilibrium opinions is minimized. We prove that the objective function is in general non-convex. Hence, formulating the problem as a convex program as in an early version of this work (Abebe et al., KDD'18) might have potential correctness issues. We instead analyze the structure of the objective function, and show that any local optimum is also a global optimum, which is somehow surprising as the objective function might not be convex. Furthermore, we combine the iterative process and the local search paradigm to design very efficient algorithms that can solve the unbudgeted variant of the problem optimally on large-scale graphs containing millions of nodes. Finally, we propose and evaluate experimentally a family of heuristics for the budgeted variation of the problem.

cs.SI

Communication Complexity of Byzantine Agreement, Revisited

As Byzantine Agreement (BA) protocols find application in large-scale decentralized cryptocurrencies, an increasingly important problem is to design BA protocols with improved communication complexity. A few existing works have shown how to achieve subquadratic BA under an {\it adaptive} adversary. Intriguingly, they all make a common relaxation about the adaptivity of the attacker, that is, if an honest node sends a message and then gets corrupted in some round, the adversary {\it cannot erase the message that was already sent} --- henceforth we say that such an adversary cannot perform "after-the-fact removal". By contrast, many (super-)quadratic BA protocols in the literature can tolerate after-the-fact removal. In this paper, we first prove that disallowing after-the-fact removal is necessary for achieving subquadratic-communication BA. Next, we show new subquadratic binary BA constructions (of course, assuming no after-the-fact removal) that achieves near-optimal resilience and expected constant rounds under standard cryptographic assumptions and a public-key infrastructure (PKI) in both synchronous and partially synchronous settings. In comparison, all known subquadratic protocols make additional strong assumptions such as random oracles or the ability of honest nodes to erase secrets from memory, and even with these strong assumptions, no prior work can achieve the above properties. Lastly, we show that some setup assumption is necessary for achieving subquadratic multicast-based BA.

cs.DC

Small Memory Robust Simulation of Client-Server Interactive Protocols over Oblivious Noisy Channels

We revisit the problem of low-memory robust simulation of interactive protocols over noisy channels. Haeupler [FOCS 2014] considered robust simulation of two-party interactive protocols over oblivious, as well as adaptive, noisy channels. Since the simulation does not need to have fixed communication pattern, the achieved communication rates can circumvent the lower bound proved by Kol and Raz [STOC 2013]. However, a drawback of this approach is that each party needs to remember the whole history of the simulated transcript. In a subsequent manuscript, Haeupler and Resch considered low-memory simulation. The idea was to view the original protocol as a computational DAG and only the identities of the nodes are saved (as opposed to the whole transcript history) for backtracking to reduce memory usage. In this paper, we consider low-memory robust simulation of more general client-server interactive protocols, in which a leader communicates with other members/servers, who do not communicate among themselves; this setting can be applied to information-theoretic multi-server Private Information Retrieval (PIR) schemes. We propose an information-theoretic technique that converts any correct PIR protocol that assumes reliable channels, into a protocol which is both correct and private in the presence of a noisy channel while keeping the space complexity to a minimum. Despite the huge attention that PIR protocols have received in the literature, the existing works assume that the parties communicate using noiseless channels.

cs.IT

More is Less: Perfectly Secure Oblivious Algorithms in the Multi-Server Setting

The problem of Oblivious RAM (ORAM) has traditionally been studied in a single-server setting, but more recently the multi-server setting has also been considered. Yet it is still unclear whether the multi-server setting has any inherent advantages, e.g., whether the multi-server setting can be used to achieve stronger security goals or provably better efficiency than is possible in the single-server case. In this work, we construct a perfectly secure 3-server ORAM scheme that outperforms the best known single-server scheme by a logarithmic factor. In the process, we also show, for the first time, that there exist specific algorithms for which multiple servers can overcome known lower bounds in the single-server setting.

cs.CR

A Unified PTAS for Prize Collecting TSP and Steiner Tree Problem in Doubling Metrics

We present a unified polynomial-time approximation scheme (PTAS) for the prize collecting traveling salesman problem (PCTSP) and the prize collecting Steiner tree problem (PCSTP) in doubling metrics. Given a metric space and a penalty function on a subset of points known as terminals, a solution is a subgraph on points in the metric space, whose cost is the weight of its edges plus the penalty due to terminals not covered by the subgraph. Under our unified framework, the solution subgraph needs to be Eulerian for PCTSP, while it needs to be connected for PCSTP. Before our work, even a QPTAS for the problems in doubling metrics is not known. Our unified PTAS is based on the previous dynamic programming frameworks proposed in [Talwar STOC 2004] and [Bartal, Gottlieb, Krauthgamer STOC 2012]. However, since it is unknown which part of the optimal cost is due to edge lengths and which part is due to penalties of uncovered terminals, we need to develop new techniques to apply previous divide-and-conquer strategies and sparse instance decompositions.

cs.DS