arXiv subjects

Patrick Jaillet

Publications and source records attributed to Patrick Jaillet.

At least 37 records · Page 2Linked to original sources

arXiv2025

Market Design for Capacity Sharing in Networks

We study a market mechanism that sets edge prices to incentivize strategic agents to efficiently share limited network capacity. In this market, agents form coalitions, with each coalition sharing a unit capacity of a selected route and making payments to cover edge prices. Our focus is on the existence and computation of market equilibrium, where challenges arise from the interdependence between coalition formation among strategic agents with heterogeneous preferences and route selection that induces a network flow under integral capacity constraints. To address this interplay between coalition formation and network capacity utilization, we introduce a novel approach based on combinatorial auction theory and network flow theory. We establish sufficient conditions on the network topology and agents' preferences that guarantee both the existence and polynomial-time computation of a market equilibrium. Additionally, we identify a particular market equilibrium that maximizes utilities for all agents and the outcome is equivalent to the classical Vickrey-Clarke-Groves mechanism. Furthermore, we extend our results to multi-period settings and general networks, showing that when the sufficient conditions are not met, an equilibrium may still exist but requires more complex, path-based pricing mechanisms that set differentiated prices based on agents' preference parameters.

cs.GT↗

arXiv2025

Double Machine Learning Based Structure Identification from Temporal Data

Learning the causes of time-series data is a fundamental task in many applications, spanning from finance to earth sciences or bio-medical applications. Common approaches for this task are based on vector auto-regression, and they do not take into account unknown confounding between potential causes. However, in settings with many potential causes and noisy data, these approaches may be substantially biased. Furthermore, potential causes may be correlated in practical applications or even contain cycles. To address these challenges, we propose a new double machine learning based method for structure identification from temporal data (DR-SIT). We provide theoretical guarantees, showing that our method asymptotically recovers the true underlying causal structure. Our analysis extends to cases where the potential causes have cycles, and they may even be confounded. We further perform extensive experiments to showcase the superior performance of our method. Code: https://github.com/sdi1100041/TMLR_submission_DR_SIT

cs.LG↗

arXiv2025

Grace Period is All You Need: Individual Fairness without Revenue Loss in Revenue Management

Imagine you and a friend purchase identical items at a store, yet only your friend received a discount. Would your friend's discount make you feel unfairly treated by the store? And would you be less willing to purchase from that store again in the future? Based on a large-scale online survey that we ran on Prolific, it turns out that the answers to the above questions are positive. Therefore, when allocating resources to different customers, sellers should consider both the total reward and individual fairness. Motivated by these findings, in this work we propose a notion of individual fairness in online revenue management and an algorithmic module (called ``Grace Period'') that can be embedded in traditional revenue management algorithms and guarantee individual fairness. Specifically, we show how to embed the Grace Period in five common revenue management algorithms including Deterministic Linear Programming with Probabilistic Assignment, Resolving Deterministic Linear Programming with Probabilistic Assignment, Static Bid Price Control, Booking Limit, and Nesting, thus covering both stochastic and adversarial customer arrival settings. Embedding the Grace Period does not incur additional regret for any of these algorithms. This finding indicates that, in an asymptotic regime, there is no tradeoff between a seller maximizing their revenue and guaranteeing that each customer feels fairly treated. The core intuition behind the Grace Period is that independent randomized decisions for each customer often lead to unfair outcomes. However, we cannot eliminate the randomness, as it plays a crucial role in maximizing profit. The Grace Period addresses this by shifting randomness away from individual decisions and applying it instead to the total number of customers receiving a particular decision. This approach preserves revenue potential while mitigating fairness issues.

cs.GT↗

arXiv2025

Neural Dueling Bandits: Preference-Based Optimization with Human Feedback

Contextual dueling bandit is used to model the bandit problems, where a learner's goal is to find the best arm for a given context using observed noisy human preference feedback over the selected arms for the past contexts. However, existing algorithms assume the reward function is linear, which can be complex and non-linear in many real-life applications like online recommendations or ranking web search results. To overcome this challenge, we use a neural network to estimate the reward function using preference feedback for the previously selected arms. We propose upper confidence bound- and Thompson sampling-based algorithms with sub-linear regret guarantees that efficiently select arms in each round. We also extend our theoretical results to contextual bandit problems with binary feedback, which is in itself a non-trivial contribution. Experimental results on the problem instances derived from synthetic datasets corroborate our theoretical results.

cs.LG↗

arXiv2025

Learning with Exact Invariances in Polynomial Time

We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either fail to provide a polynomial-time solution or are not applicable in the kernel setting. However, with oracle access to the geometric properties of the input space, we propose a polynomial-time algorithm that learns a classifier with \emph{exact} invariances. Moreover, our approach achieves the same excess population risk (or generalization error) as the original kernel regression problem. To the best of our knowledge, this is the first polynomial-time algorithm to achieve exact (not approximate) invariances in this context. Our proof leverages tools from differential geometry, spectral theory, and optimization. A key result in our development is a new reformulation of the problem of learning under invariances as optimizing an infinite number of linearly constrained convex quadratic programs, which may be of independent interest.

cs.LG↗

arXiv2024

Prompt Optimization with EASE? Efficient Ordering-aware Automated Selection of Exemplars

Large language models (LLMs) have shown impressive capabilities in real-world applications. The capability of in-context learning (ICL) allows us to adapt an LLM to downstream tasks by including input-label exemplars in the prompt without model fine-tuning. However, the quality of these exemplars in the prompt greatly impacts performance, highlighting the need for an effective automated exemplar selection method. Recent studies have explored retrieval-based approaches to select exemplars tailored to individual test queries, which can be undesirable due to extra test-time computation and an increased risk of data exposure. Moreover, existing methods fail to adequately account for the impact of exemplar ordering on the performance. On the other hand, the impact of the instruction, another essential component in the prompt given to the LLM, is often overlooked in existing exemplar selection methods. To address these challenges, we propose a novel method named EASE, which leverages the hidden embedding from a pre-trained language model to represent ordered sets of exemplars and uses a neural bandit algorithm to optimize the sets of exemplars while accounting for exemplar ordering. Our EASE can efficiently find an ordered set of exemplars that performs well for all test queries from a given task, thereby eliminating test-time computation. Importantly, EASE can be readily extended to jointly optimize both the exemplars and the instruction. Through extensive empirical evaluations (including novel tasks), we demonstrate the superiority of EASE over existing methods, and reveal practical insights about the impact of exemplar selection on ICL, which may be of independent interest. Our code is available at https://github.com/ZhaoxuanWu/EASE-Prompt-Optimization.

cs.AI↗

arXiv2024

Use Your INSTINCT: INSTruction optimization for LLMs usIng Neural bandits Coupled with Transformers

Large language models (LLMs) have shown remarkable instruction-following capabilities and achieved impressive performances in various applications. However, the performances of LLMs depend heavily on the instructions given to them, which are typically manually tuned with substantial human efforts. Recent work has used the query-efficient Bayesian optimization (BO) algorithm to automatically optimize the instructions given to black-box LLMs. However, BO usually falls short when optimizing highly sophisticated (e.g., high-dimensional) objective functions, such as the functions mapping an instruction to the performance of an LLM. This is mainly due to the limited expressive power of the Gaussian process (GP) which is used by BO as a surrogate to model the objective function. Meanwhile, it has been repeatedly shown that neural networks (NNs), especially pre-trained transformers, possess strong expressive power and can model highly complex functions. So, we adopt a neural bandit algorithm which replaces the GP in BO by an NN surrogate to optimize instructions for black-box LLMs. More importantly, the neural bandit algorithm allows us to naturally couple the NN surrogate with the hidden representation learned by a pre-trained transformer (i.e., an open-source LLM), which significantly boosts its performance. These motivate us to propose our INSTruction optimization usIng Neural bandits Coupled with Transformers (INSTINCT) algorithm. We perform instruction optimization for ChatGPT and use extensive experiments to show that INSTINCT consistently outperforms baselines in different tasks, e.g., various instruction induction tasks and the task of improving zero-shot chain-of-thought instructions. Our code is available at https://github.com/xqlin98/INSTINCT.

cs.LG↗

arXiv2024

A Universal Class of Sharpness-Aware Minimization Algorithms

Recently, there has been a surge in interest in developing optimization algorithms for overparameterized models as achieving generalization is believed to require algorithms with suitable biases. This interest centers on minimizing sharpness of the original loss function; the Sharpness-Aware Minimization (SAM) algorithm has proven effective. However, most literature only considers a few sharpness measures, such as the maximum eigenvalue or trace of the training loss Hessian, which may not yield meaningful insights for non-convex optimization scenarios like neural networks. Additionally, many sharpness measures are sensitive to parameter invariances in neural networks, magnifying significantly under rescaling parameters. Motivated by these challenges, we introduce a new class of sharpness measures in this paper, leading to new sharpness-aware objective functions. We prove that these measures are \textit{universally expressive}, allowing any function of the training loss Hessian matrix to be represented by appropriate hyperparameters. Furthermore, we show that the proposed objective functions explicitly bias towards minimizing their corresponding sharpness measures, and how they allow meaningful applications to models with parameter invariances (such as scale-invariances). Finally, as instances of our proposed general framework, we present \textit{Frob-SAM} and \textit{Det-SAM}, which are specifically designed to minimize the Frobenius norm and the determinant of the Hessian of the training loss, respectively. We also demonstrate the advantages of our general framework through extensive experiments.

cs.LG↗

arXiv2024

Prompt Optimization with Human Feedback

Large language models (LLMs) have demonstrated remarkable performances in various tasks. However, the performance of LLMs heavily depends on the input prompt, which has given rise to a number of recent works on prompt optimization. However, previous works often require the availability of a numeric score to assess the quality of every prompt. Unfortunately, when a human user interacts with a black-box LLM, attaining such a score is often infeasible and unreliable. Instead, it is usually significantly easier and more reliable to obtain preference feedback from a human user, i.e., showing the user the responses generated from a pair of prompts and asking the user which one is preferred. Therefore, in this paper, we study the problem of prompt optimization with human feedback (POHF), in which we aim to optimize the prompt for a black-box LLM using only human preference feedback. Drawing inspiration from dueling bandits, we design a theoretically principled strategy to select a pair of prompts to query for preference feedback in every iteration, and hence introduce our algorithm named automated POHF (APOHF). We apply our APOHF algorithm to various tasks, including optimizing user instructions, prompt optimization for text-to-image generative models, and response optimization with human feedback (i.e., further refining the response using a variant of our APOHF). The results demonstrate that our APOHF can efficiently find a good prompt using a small number of preference feedback instances. Our code can be found at \url{https://github.com/xqlin98/APOHF}.

cs.LG↗

arXiv2024

Incentives in Private Collaborative Machine Learning

Collaborative machine learning involves training models on data from multiple parties but must incentivize their participation. Existing data valuation methods fairly value and reward each party based on shared data or model parameters but neglect the privacy risks involved. To address this, we introduce differential privacy (DP) as an incentive. Each party can select its required DP guarantee and perturb its sufficient statistic (SS) accordingly. The mediator values the perturbed SS by the Bayesian surprise it elicits about the model parameters. As our valuation function enforces a privacy-valuation trade-off, parties are deterred from selecting excessive DP guarantees that reduce the utility of the grand coalition's model. Finally, the mediator rewards each party with different posterior samples of the model parameters. Such rewards still satisfy existing incentives like fairness but additionally preserve DP and a high similarity to the grand coalition's posterior. We empirically demonstrate the effectiveness and practicality of our approach on synthetic and real-world datasets.

cs.LG↗

arXiv2024

When Should you Offer an Upgrade: Online Upgrading Mechanisms for Resource Allocation

In this work, we study an upgrading scheme for online resource allocation problems. We work in a sequential setting, where at each round a request for a resource arrives and the decision-maker has to decide whether to accept it (and thus, offer the resource) or reject it. The resources are ordered in terms of their value. If the decision-maker decides to accept the request, they can offer an upgrade-for-a-fee to the next more valuable resource. This fee is dynamically decided based on the currently available resources. After the upgrade-for-a-fee option is presented to the requester, they can either accept it, get upgraded, and pay the additional fee, or reject it and maintain their originally allocated resource. We take the perspective of the decision-maker and wish to design upgrading mechanisms in a way that simultaneously maximizes revenue and minimizes underutilization of resources. Both of these desiderata are encapsulated in a notion of regret that we define, and according to which we measure our algorithms' performance. We present a fast algorithm that achieves O(log T) regret. Finally, we implemented our algorithm utilizing data akin to those observed in the hospitality industry and estimated our upgrading mechanism would increase the annual revenue by over 17%.

math.OC↗

arXiv2023

Information Design for Hybrid Work under Infectious Disease Transmission Risk

We study a planner's provision of information to manage workplace occupancy when strategic workers (agents) face risk of infectious disease transmission. The planner implements an information mechanism to signal information about the underlying risk of infection at the workplace. Agents update their belief over the risk parameter using this information and choose to work in-person or remotely. We address the design of the optimal signaling mechanism that best aligns the workplace occupancy with the planner's preference (i.e., maintaining safe capacity limits and operational efficiency at workplace). For various forms of planner preferences, we show numerical and analytical proof that interval-based information mechanisms are optimal. These mechanisms partition the continuous domain of the risk parameter into disjoint intervals and provision information based on interval-specific probability distributions over a finite set of signals. When the planner seeks to achieve an occupancy that lies in one of finitely many pre-specified ranges independent of the underlying risk, we provide an optimal mechanism that uses at most two intervals. On the other hand, when the preference on the occupancy is risk-dependent, we show that an approximately optimal interval-based mechanism can be computed efficiently. We bound the approximation loss for preferences that are expressed through a Lipschitz continuous function of both occupancy and risk parameter. We provide examples that demonstrate the improvement of proposed signaling mechanisms relative to the common benchmarks in information provision. Our findings suggest that information provision over the risk of disease transmission is an effective intervention for maintaining desirable occupancy levels at the workplace.

cs.GT↗

arXiv2023

Batch Bayesian Optimization for Replicable Experimental Design

Many real-world experimental design problems (a) evaluate multiple experimental conditions in parallel and (b) replicate each condition multiple times due to large and heteroscedastic observation noise. Given a fixed total budget, this naturally induces a trade-off between evaluating more unique conditions while replicating each of them fewer times vs. evaluating fewer unique conditions and replicating each more times. Moreover, in these problems, practitioners may be risk-averse and hence prefer an input with both good average performance and small variability. To tackle both challenges, we propose the Batch Thompson Sampling for Replicable Experimental Design (BTS-RED) framework, which encompasses three algorithms. Our BTS-RED-Known and BTS-RED-Unknown algorithms, for, respectively, known and unknown noise variance, choose the number of replications adaptively rather than deterministically such that an input with a larger noise variance is replicated more times. As a result, despite the noise heteroscedasticity, both algorithms enjoy a theoretical guarantee and are asymptotically no-regret. Our Mean-Var-BTS-RED algorithm aims at risk-averse optimization and is also asymptotically no-regret. We also show the effectiveness of our algorithms in two practical real-world applications: precision agriculture and AutoML.

cs.LG↗

arXiv2023

Secretary Problems with Random Number of Candidates: How Prior Distributional Information Helps

We study variants of the secretary problem, where $N$, the number of candidates, is a random variable, and the decision maker wants to maximize the probability of success -- picking the largest number among the $N$ candidates -- using only the relative ranks of the candidates revealed so far. We consider three forms of prior information about $\mathbf p$, the probability distribution of $N$. In the full information setting, we assume $\mathbf p$ to be fully known. In that case, we show that single-threshold type of strategies can achieve $1/e$-approximation to the maximum probability of success among all possible strategies. In the upper bound setting, we assume that $N\leq \overline{n}$ (or $\mathbb E[N]\leq \barμ$), where $\bar{n}$ (or $\barμ$) is known. In that case, we show that randomization over single-threshold type of strategies can achieve the optimal worst case probability of success of $\frac{1}{\log(\bar{n})}$ (or $\frac{1}{\log(\barμ)}$) asymptotically. Surprisingly, there is a single-threshold strategy (depending on $\overline{n}$) that can succeed with probability $2/e^2$ for all but an exponentially small fraction of distributions supported on $[\bar{n}]$. In the sampling setting, we assume that we have access to $m$ samples $N^{(1)},\ldots,N^{(m)}\sim_{iid} \mathbf p$. In that case, we show that if $N\leq T$ with probability at least $1-O(ε)$ for some $T\in \mathbb N$, $m\gtrsim \frac{1}{ε^2}\max(\log(\frac{1}ε),ε\log(\frac{\log(T)}ε))$ is enough to learn a strategy that is at least $ε$-suboptimal, and we provide a lower bound of $Ω(\frac{1}{ε^2})$, showing that the sampling algorithm is optimal when $ε=O(\frac{1}{\log\log(T)})$.

cs.DS↗

arXiv2023

Quantum Bayesian Optimization

Kernelized bandits, also known as Bayesian optimization (BO), has been a prevalent method for optimizing complicated black-box reward functions. Various BO algorithms have been theoretically shown to enjoy upper bounds on their cumulative regret which are sub-linear in the number T of iterations, and a regret lower bound of Omega(sqrt(T)) has been derived which represents the unavoidable regrets for any classical BO algorithm. Recent works on quantum bandits have shown that with the aid of quantum computing, it is possible to achieve tighter regret upper bounds better than their corresponding classical lower bounds. However, these works are restricted to either multi-armed or linear bandits, and are hence not able to solve sophisticated real-world problems with non-linear reward functions. To this end, we introduce the quantum-Gaussian process-upper confidence bound (Q-GP-UCB) algorithm. To the best of our knowledge, our Q-GP-UCB is the first BO algorithm able to achieve a regret upper bound of O(polylog T), which is significantly smaller than its regret lower bound of Omega(sqrt(T)) in the classical setting. Moreover, thanks to our novel analysis of the confidence ellipsoid, our Q-GP-UCB with the linear kernel achieves a smaller regret than the quantum linear UCB algorithm from the previous work. We use simulations, as well as an experiment using a real quantum computer, to verify that the theoretical quantum speedup achieved by our Q-GP-UCB is also potentially relevant in practice.

cs.LG↗

arXiv2023

DRCFS: Doubly Robust Causal Feature Selection

Knowing the features of a complex system that are highly relevant to a particular target variable is of fundamental interest in many areas of science. Existing approaches are often limited to linear settings, sometimes lack guarantees, and in most cases, do not scale to the problem at hand, in particular to images. We propose DRCFS, a doubly robust feature selection method for identifying the causal features even in nonlinear and high dimensional settings. We provide theoretical guarantees, illustrate necessary conditions for our assumptions, and perform extensive experiments across a wide range of simulated and semi-synthetic datasets. DRCFS significantly outperforms existing state-of-the-art methods, selecting robust features even in challenging highly non-linear and high-dimensional problems.

cs.LG↗

arXiv2023

Memory-Constrained Algorithms for Convex Optimization via Recursive Cutting-Planes

We propose a family of recursive cutting-plane algorithms to solve feasibility problems with constrained memory, which can also be used for first-order convex optimization. Precisely, in order to find a point within a ball of radius $ε$ with a separation oracle in dimension $d$ -- or to minimize $1$-Lipschitz convex functions to accuracy $ε$ over the unit ball -- our algorithms use $\mathcal O(\frac{d^2}{p}\ln \frac{1}ε)$ bits of memory, and make $\mathcal O((C\frac{d}{p}\ln \frac{1}ε)^p)$ oracle calls, for some universal constant $C \geq 1$. The family is parametrized by $p\in[d]$ and provides an oracle-complexity/memory trade-off in the sub-polynomial regime $\ln\frac{1}ε\gg\ln d$. While several works gave lower-bound trade-offs (impossibility results) -- we explicit here their dependence with $\ln\frac{1}ε$, showing that these also hold in any sub-polynomial regime -- to the best of our knowledge this is the first class of algorithms that provides a positive trade-off between gradient descent and cutting-plane methods in any regime with $ε\leq 1/\sqrt d$. The algorithms divide the $d$ variables into $p$ blocks and optimize over blocks sequentially, with approximate separation vectors constructed using a variant of Vaidya's method. In the regime $ε\leq d^{-Ω(d)}$, our algorithm with $p=d$ achieves the information-theoretic optimal memory usage and improves the oracle-complexity of gradient descent.

math.OC↗

arXiv2023

Individual Welfare Guarantees in the Autobidding World with Machine-learned Advice

Online advertising channels have commonly focused on maximizing total advertiser value (or welfare) to enhance long-run retention and channel healthiness. Previous literature has studied auction design by incorporating machine learning predictions on advertiser values (also known as machine-learned advice) through various forms to improve total welfare. Yet, such improvements could come at the cost of individual bidders' welfare and do not shed light on how particular advertiser bidding strategies impact welfare. Motivated by this, we present an analysis on an individual bidder's welfare loss in the autobidding world for auctions with and without machine-learned advice, and also uncover how advertiser strategies relate to such losses. In particular, we demonstrate how ad platforms can utilize ML advice to improve welfare guarantee on the aggregate and individual bidder level by setting ML advice as personalized reserve prices when the platform consists of autobidders who maximize value while respecting a return-on-ad spent (ROAS) constraint. Under parallel VCG auctions with such ML advice-based reserves, we present a worst-case welfare lower-bound guarantee for an individual autobidder, and show that the lower-bound guarantee is positively correlated with ML advice quality as well the scale of bids induced by the autobidder's bidding strategies. Further, we prove an impossibility result showing that no truthful, and possibly randomized mechanism with anonymous allocations can achieve universally better individual welfare guarantees than VCG, in presence of personalized reserves based on ML-advice of equal quality. Moreover, we extend our individual welfare guarantee results to generalized first price (GFP) and generalized second price (GSP) auctions.

cs.GT↗