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Haihao Lu

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8 papers

2 author rows

ICML Conference 2024 Conference Paper

A Field Guide for Pacing Budget and ROS Constraints

Santiago R. Balseiro
Kshipra Bhawalkar
Zhe Feng 0004
Haihao Lu
Vahab Mirrokni
Balasubramanian Sivan
Di Wang 0005

Budget pacing is a popular service that has been offered by major internet advertising platforms since their inception. In the past few years, autobidding products that provide real-time bidding as a service to advertisers have seen a prominent rise in adoption. A popular autobidding stategy is value maximization subject to return-on-spend (ROS) constraints. For historical or business reasons, the systems that govern these two services, namely budget pacing and ROS pacing, are not necessarily always a single unified and coordinated entity that optimizes a global objective subject to both constraints. The purpose of this work is to theoretically and empirically compare algorithms with different degrees of coordination between these two pacing systems. In particular, we compare (a) a fully-decoupled sequential algorithm; (b) a minimally-coupled min-pacing algorithm; (c) a fully-coupled dual-based algorithm. Our main contribution is to theoretically analyze the min-pacing algorithm and show that it attains similar guarantees to the fully-coupled canonical dual-based algorithm. On the other hand, we show that the sequential algorithm, even though appealing by virtue of being fully decoupled, could badly violate the constraints. We validate our theoretical findings empirically by showing that the min-pacing algorithm performs almost as well as the canonical dual-based algorithm on a semi-synthetic dataset that was generated from a large online advertising platform’s auction data.

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NeurIPS Conference 2023 Conference Paper

Online Ad Procurement in Non-stationary Autobidding Worlds

Jason Cheuk Nam Liang
Haihao Lu
Baoyu Zhou

Today's online advertisers procure digital ad impressions through interacting with autobidding platforms: advertisers convey high level procurement goals via setting levers such as budget, target return-on-investment, max cost per click, etc. . Then ads platforms subsequently procure impressions on advertisers' behalf, and report final procurement conversions (e. g. click) to advertisers. In practice, advertisers may receive minimal information on platforms' procurement details, and procurement outcomes are subject to non-stationary factors like seasonal patterns, occasional system corruptions, and market trends which make it difficult for advertisers to optimize lever decisions effectively. Motivated by this, we present an online learning framework that helps advertisers dynamically optimize ad platform lever decisions while subject to general long-term constraints in a realistic bandit feedback environment with non-stationary procurement outcomes. In particular, we introduce a primal-dual algorithm for online decision making with multi-dimension decision variables, bandit feedback and long-term uncertain constraints. We show that our algorithm achieves low regret in many worlds when procurement outcomes are generated through procedures that are stochastic, adversarial, adversarially corrupted, periodic, and ergodic, respectively, without having to know which procedure is the ground truth. Finally, we emphasize that our proposed algorithm and theoretical results extend beyond the applications of online advertising.

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NeurIPS Conference 2021 Conference Paper

Practical Large-Scale Linear Programming using Primal-Dual Hybrid Gradient

David Applegate
Mateo Diaz
Oliver Hinder
Haihao Lu
Miles Lubin
Brendan O'Donoghue
Warren Schudy

We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core operation is matrix-vector multiplications. PDLP is derived by applying the primal-dual hybrid gradient (PDHG) method, popularized by Chambolle and Pock (2011), to a saddle-point formulation of LP. PDLP enhances PDHG for LP by combining several new techniques with older tricks from the literature; the enhancements include diagonal preconditioning, presolving, adaptive step sizes, and adaptive restarting. PDLP improves the state of the art for first-order methods applied to LP. We compare PDLP with SCS, an ADMM-based solver, on a set of 383 LP instances derived from MIPLIB 2017. With a target of $10^{-8}$ relative accuracy and 1 hour time limit, PDLP achieves a 6. 3x reduction in the geometric mean of solve times and a 4. 6x reduction in the number of instances unsolved (from 227 to 49). Furthermore, we highlight standard benchmark instances and a large-scale application (PageRank) where our open-source prototype of PDLP, written in Julia, outperforms a commercial LP solver.

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ICML Conference 2021 Conference Paper

Regularized Online Allocation Problems: Fairness and Beyond

Santiago R. Balseiro
Haihao Lu
Vahab Mirrokni

Online allocation problems with resource constraints have a rich history in computer science and operations research. In this paper, we introduce the regularized online allocation problem, a variant that includes a non-linear regularizer acting on the total resource consumption. In this problem, requests repeatedly arrive over time and, for each request, a decision maker needs to take an action that generates a reward and consumes resources. The objective is to simultaneously maximize total rewards and the value of the regularizer subject to the resource constraints. Our primary motivation is the online allocation of internet advertisements wherein firms seek to maximize additive objectives such as the revenue or efficiency of the allocation. By introducing a regularizer, firms can account for the fairness of the allocation or, alternatively, punish under-delivery of advertisements—two common desiderata in internet advertising markets. We design an algorithm when arrivals are drawn independently from a distribution that is unknown to the decision maker. Our algorithm is simple, fast, and attains the optimal order of sub-linear regret compared to the optimal allocation with the benefit of hindsight. Numerical experiments confirm the effectiveness of the proposed algorithm and of the regularizers in an internet advertising application.

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NeurIPS Conference 2020 Conference Paper

Contextual Reserve Price Optimization in Auctions via Mixed Integer Programming

Joey Huchette
Haihao Lu
Hossein Esfandiari
Vahab Mirrokni

We study the problem of learning a linear model to set the reserve price in an auction, given contextual information, in order to maximize expected revenue from the seller side. First, we show that it is not possible to solve this problem in polynomial time unless the Exponential Time Hypothesis fails. Second, we present a strong mixed-integer programming (MIP) formulation for this problem, which is capable of exactly modeling the nonconvex and discontinuous expected reward function. Moreover, we show that this MIP formulation is ideal (i. e. the strongest possible formulation) for the revenue function of a single impression. Since it can be computationally expensive to exactly solve the MIP formulation in practice, we also study the performance of its linear programming (LP) relaxation. Though it may work well in practice, we show that, unfortunately, in the worst case the optimal objective of the LP relaxation can be O(number of samples) times larger than the optimal objective of the true problem. Finally, we present computational results, showcasing that the MIP formulation, along with its LP relaxation, are able to achieve superior in- and out-of-sample performance, as compared to state-of-the-art algorithms on both real and synthetic datasets. More broadly, we believe this work offers an indication of the strength of optimization methodologies like MIP to exactly model intrinsic discontinuities in machine learning problems.

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ICML Conference 2020 Conference Paper

Dual Mirror Descent for Online Allocation Problems

Santiago R. Balseiro
Haihao Lu
Vahab Mirrokni

We consider online allocation problems with concave revenue functions and resource constraints, which are central problems in revenue management and online advertising. In these settings, requests arrive sequentially during a finite horizon and, for each request, a decision maker needs to choose an action that consumes a certain amount of resources and generates revenue. The revenue function and resource consumption of each request are drawn independently and at random from a probability distribution that is unknown to the decision maker. The objective is to maximize cumulative revenues subject to a constraint on the total consumption of resources. We design a general class of algorithms that achieve sub-linear expected regret compared to the hindsight optimal allocation. Our algorithms operate in the Lagrangian dual space: they maintain a dual multiplier for each resource that is updated using online mirror descent. By choosing the reference function accordingly, we recover dual sub-gradient descent and dual exponential weights algorithm. The resulting algorithms are simple, efficient, and shown to attain the optimal order of regret when the length of the horizon and the initial number of resources are scaled proportionally. We discuss applications to online bidding in repeated auctions with budget constraints and online proportional matching with high entropy.

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ICML Conference 2018 Conference Paper

Accelerating Greedy Coordinate Descent Methods

Haihao Lu
Robert M. Freund
Vahab Mirrokni

We introduce and study two algorithms to accelerate greedy coordinate descent in theory and in practice: Accelerated Semi-Greedy Coordinate Descent (ASCD) and Accelerated Greedy Coordinate Descent (AGCD). On the theory side, our main results are for ASCD: we show that ASCD achieves $O(1/k^2)$ convergence, and it also achieves accelerated linear convergence for strongly convex functions. On the empirical side, while both AGCD and ASCD outperform Accelerated Randomized Coordinate Descent on most instances in our numerical experiments, we note that AGCD significantly outperforms the other two methods in our experiments, in spite of a lack of theoretical guarantees for this method. To complement this empirical finding for AGCD, we present an explanation why standard proof techniques for acceleration cannot work for AGCD, and we further introduce a technical condition under which AGCD is guaranteed to have accelerated convergence. Finally, we confirm that this technical condition holds in our numerical experiments.

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ICML Conference 2018 Conference Paper

Approximate Leave-One-Out for Fast Parameter Tuning in High Dimensions

Shuaiwen Wang
Wenda Zhou
Haihao Lu
Arian Maleki
Vahab Mirrokni

We study the parameter tuning problem for the penalized regression model. Finding the optimal choice of the regularization parameter is a challenging problem in high-dimensional regimes where both the number of observations n and the number of parameters p are large. We propose two frameworks to obtain a computationally efficient approximation ALO of the leave-one-out cross validation (LOOCV) risk for nonsmooth losses and regularizers. Our two frameworks are based on the primal and dual formulations of the penalized regression model. We prove the equivalence of the two approaches under smoothness conditions. This equivalence enables us to justify the accuracy of both methods under such conditions. We use our approaches to obtain a risk estimate for several standard problems, including generalized LASSO, nuclear norm regularization and support vector machines. We experimentally demonstrate the effectiveness of our results for non-differentiable cases.

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