arXiv subjects

Siddharth Prasad

Publications and source records attributed to Siddharth Prasad.

14 recordsLinked to original sources

arXiv2026

Parameter Tuning with Generalization Guarantees for GPU-Accelerated Linear Programming

Recent research has developed practical, parallelizable first-order methods for large scale linear programming, but performance is highly dependent on hyperparameter selection. We derive generalization guarantees for hyperparameter tuning within (cu)PDLP, a state-of-the-art first-order LP solver designed for modern hardware. First, we pin down the behavior of PDHG, the primal-dual hybrid gradient algorithm that underlies PDLP, as a function of its step size and primal weight, leading to linear sample complexity guarantees for learning those parameters. We then conduct a structural analysis of PDLP, which augments PDHG with several specialized techniques like preconditioning, adaptive step sizes, averaging, adaptive restarts, and smoothed primal weight updates. Our analysis captures the behavior of the solution trajectory as a function of the hyperparameters and leverages recent advances in data-driven algorithm design to obtain polynomial sample complexity guarantees for learning those hyperparameters. Finally, we conduct proof-of-concept experiments that demonstrate the need for data-driven PDLP parameter tuning. Our results showcase the versatility of the data-driven algorithm design toolkit for principled hyperparameter tuning within solver-grade implementations of complex modern optimization algorithms.

math.OC↗

arXiv2026

In-Context Credit Assignment via the Core

We propose incentive-aligned mechanisms for in-context credit assignment: the task of assigning credit for AI-generated content (e.g. code, news articles, short-form videos) among creators whose intellectual property appears in the context window. Our approach is based on the least core solution concept from cooperative game theory, which distributes value in a way that is as stable as possible by ensuring that no subset of creators is significantly under-compensated relative to the value they could generate on their own. We develop algorithms for approximating the least core, which leverage novel routines for constraint seeding and constraint separation. On a web retrieval credit assignment task, we find that our approaches are capable of approximating the least core using orders of magnitude fewer LLM calls compared to alternative methods.

cs.GT↗

arXiv2025

Weakest Bidder Types and New Core-Selecting Combinatorial Auctions

Core-selecting combinatorial auctions are popular auction designs that constrain prices to eliminate the incentive for any group of bidders -- with the seller -- to renegotiate for a better deal. They help overcome the low-revenue issues of classical combinatorial auctions. We introduce a new class of core-selecting combinatorial auctions that leverage bidder information available to the auction designer. We model such information through constraints on the joint type space of the bidders -- these are constraints on bidders' private valuations that are known to hold by the auction designer before bids are elicited. First, we show that type space information can overcome the well-known impossibility of incentive-compatible core-selecting combinatorial auctions. We present a revised and generalized version of that impossibility result that depends on how much information is conveyed by the type spaces. We then devise a new family of core-selecting combinatorial auctions and show that they minimize the sum of bidders' incentives to deviate from truthful bidding. We develop new constraint generation techniques -- and build upon existing quadratic programming techniques -- to compute core prices, and conduct experiments to evaluate the incentive, revenue, fairness, and computational merits of our new auctions. Our new core-selecting auctions directly improve upon existing designs that have been used in many high-stakes auctions around the world. We envision that they will be a useful addition to any auction designer's toolkit.

cs.GT↗

arXiv2025

Revenue-Optimal Efficient Mechanism Design with General Type Spaces

We derive the revenue-optimal efficient (welfare-maximizing) mechanism in a general multidimensional mechanism design setting when type spaces -- that is, the underlying domains from which agents' values come from -- can capture arbitrarily complex informational constraints about the agents. Type spaces can encode information about agents representing, for example, machine learning predictions of agent behavior, institutional knowledge about feasible market outcomes (such as item substitutability or complementarity in auctions), and correlations between multiple agents. Prior work has only dealt with connected type spaces, which are not expressive enough to capture many natural kinds of constraints such as disjunctive constraints. We provide two characterizations of the optimal mechanism based on allocations and connected components; both make use of an underlying network flow structure to the mechanism design. Our results significantly generalize and improve the prior state of the art in revenue-optimal efficient mechanism design. They also considerably expand the scope of what forms of agent information can be expressed and used to improve revenue.

cs.GT↗

arXiv2024

New Sequence-Independent Lifting Techniques for Cutting Planes and When They Induce Facets

Sequence-independent lifting is a procedure for strengthening valid inequalities of an integer program. We generalize the sequence-independent lifting method of Gu, Nemhauser, and Savelsbergh (GNS lifting) for cover inequalities and correct an error in their proposed generalization. We obtain a new sequence-independent lifting technique -- piecewise-constant (PC) lifting -- with a number of interesting properties. We derive a broad set of sufficient conditions under which PC lifting is facet defining. To our knowledge, this is the first characterization of facet-defining sequence-independent liftings that are efficiently computable from the underlying cover. Finally, we demonstrate via experiments that PC lifting can be a useful alternative to GNS lifting. We test our new lifting techniques atop a number of novel cover cut generation routines, which prove to be effective in experiments with CPLEX.

math.OC↗

arXiv2023

Content Prompting: Modeling Content Provider Dynamics to Improve User Welfare in Recommender Ecosystems

Users derive value from a recommender system (RS) only to the extent that it is able to surface content (or items) that meet their needs/preferences. While RSs often have a comprehensive view of user preferences across the entire user base, content providers, by contrast, generally have only a local view of the preferences of users that have interacted with their content. This limits a provider's ability to offer new content to best serve the broader population. In this work, we tackle this information asymmetry with content prompting policies. A content prompt is a hint or suggestion to a provider to make available novel content for which the RS predicts unmet user demand. A prompting policy is a sequence of such prompts that is responsive to the dynamics of a provider's beliefs, skills and incentives. We aim to determine a joint prompting policy that induces a set of providers to make content available that optimizes user social welfare in equilibrium, while respecting the incentives of the providers themselves. Our contributions include: (i) an abstract model of the RS ecosystem, including content provider behaviors, that supports such prompting; (ii) the design and theoretical analysis of sequential prompting policies for individual providers; (iii) a mixed integer programming formulation for optimal joint prompting using path planning in content space; and (iv) simple, proof-of-concept experiments illustrating how such policies improve ecosystem health and user welfare.

cs.MA↗

arXiv2023

Bicriteria Multidimensional Mechanism Design with Side Information

We develop a versatile methodology for multidimensional mechanism design that incorporates side information about agents to generate high welfare and high revenue simultaneously. Side information sources include advice from domain experts, predictions from machine learning models, and even the mechanism designer's gut instinct. We design a tunable mechanism that integrates side information with an improved VCG-like mechanism based on weakest types, which are agent types that generate the least welfare. We show that our mechanism, when its side information is of high quality, generates welfare and revenue competitive with the prior-free total social surplus, and its performance decays gracefully as the side information quality decreases. We consider a number of side information formats including distribution-free predictions, predictions that express uncertainty, agent types constrained to low-dimensional subspaces of the ambient type space, and the traditional setting with known priors over agent types. In each setting we design mechanisms based on weakest types and prove performance guarantees.

cs.GT↗

arXiv2022

Improved Sample Complexity Bounds for Branch-and-Cut

Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search tree that it builds, but are challenging to tune by hand. An increasingly popular approach is to use machine learning to tune these parameters: using a training set of integer programs from the application domain at hand, the goal is to find a configuration with strong predicted performance on future, unseen integer programs from the same domain. If the training set is too small, a configuration may have good performance over the training set but poor performance on future integer programs. In this paper, we prove sample complexity guarantees for this procedure, which bound how large the training set should be to ensure that for any configuration, its average performance over the training set is close to its expected future performance. Our guarantees apply to parameters that control the most important aspects of branch-and-cut: node selection, branching constraint selection, and cutting plane selection, and are sharper and more general than those found in prior research.

cs.LG↗

arXiv2022

Structural Analysis of Branch-and-Cut and the Learnability of Gomory Mixed Integer Cuts

The incorporation of cutting planes within the branch-and-bound algorithm, known as branch-and-cut, forms the backbone of modern integer programming solvers. These solvers are the foremost method for solving discrete optimization problems and thus have a vast array of applications in machine learning, operations research, and many other fields. Choosing cutting planes effectively is a major research topic in the theory and practice of integer programming. We conduct a novel structural analysis of branch-and-cut that pins down how every step of the algorithm is affected by changes in the parameters defining the cutting planes added to the input integer program. Our main application of this analysis is to derive sample complexity guarantees for using machine learning to determine which cutting planes to apply during branch-and-cut. These guarantees apply to infinite families of cutting planes, such as the family of Gomory mixed integer cuts, which are responsible for the main breakthrough speedups of integer programming solvers. We exploit geometric and combinatorial structure of branch-and-cut in our analysis, which provides a key missing piece for the recent generalization theory of branch-and-cut.

math.OC↗

arXiv2021

Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond

Cutting-plane methods have enabled remarkable successes in integer programming over the last few decades. State-of-the-art solvers integrate a myriad of cutting-plane techniques to speed up the underlying tree-search algorithm used to find optimal solutions. In this paper we prove the first guarantees for learning high-performing cut-selection policies tailored to the instance distribution at hand using samples. We first bound the sample complexity of learning cutting planes from the canonical family of Chvátal-Gomory cuts. Our bounds handle any number of waves of any number of cuts and are fine tuned to the magnitudes of the constraint coefficients. Next, we prove sample complexity bounds for more sophisticated cut selection policies that use a combination of scoring rules to choose from a family of cuts. Finally, beyond the realm of cutting planes for integer programming, we develop a general abstraction of tree search that captures key components such as node selection and variable selection. For this abstraction, we bound the sample complexity of learning a good policy for building the search tree.

cs.AI↗

arXiv2019

Incentive Compatible Active Learning

We consider active learning under incentive compatibility constraints. The main application of our results is to economic experiments, in which a learner seeks to infer the parameters of a subject's preferences: for example their attitudes towards risk, or their beliefs over uncertain events. By cleverly adapting the experimental design, one can save on the time spent by subjects in the laboratory, or maximize the information obtained from each subject in a given laboratory session; but the resulting adaptive design raises complications due to incentive compatibility. A subject in the lab may answer questions strategically, and not truthfully, so as to steer subsequent questions in a profitable direction. We analyze two standard economic problems: inference of preferences over risk from multiple price lists, and belief elicitation in experiments on choice over uncertainty. In the first setting, we tune a simple and fast learning algorithm to retain certain incentive compatibility properties. In the second setting, we provide an incentive compatible learning algorithm based on scoring rules with query complexity that differs from obvious methods of achieving fast learning rates only by subpolynomial factors. Thus, for these areas of application, incentive compatibility may be achieved without paying a large sample complexity price.

cs.GT↗

arXiv2019

New Properties of Numbers of Plane Graphs

We explore various techniques for counting the number of straight-edge crossing-free graphs that can be embedded on a planar point set. In particular, we derive a lower bound on the ratio of the number of such graphs with $m+1$ edges to the number of graphs with $m$ edges. We show how a relatively small improvement of this bound would improve existing bounds concerning numbers of plane graphs with a prescribed number of edges. Furthermore, we use a cross-graph charging scheme to derive lower bounds for the number of such graphs when the point set has few extreme points.

math.CO↗

arXiv2018

Learning Time Dependent Choice

We explore questions dealing with the learnability of models of choice over time. We present a large class of preference models defined by a structural criterion for which we are able to obtain an exponential improvement over previously known learning bounds for more general preference models. This in particular implies that the three most important discounted utility models of intertemporal choice -- exponential, hyperbolic, and quasi-hyperbolic discounting -- are learnable in the PAC setting with VC dimension that grows logarithmically in the number of time periods. We also examine these models in the framework of active learning. We find that the commonly studied stream-based setting is in general difficult to analyze for preference models, but we provide a redeeming situation in which the learner can indeed improve upon the guarantees provided by PAC learning. In contrast to the stream-based setting, we show that if the learner is given full power over the data he learns from -- in the form of learning via membership queries -- even very naive algorithms significantly outperform the guarantees provided by higher level active learning algorithms.

cs.GT↗

arXiv2014

Walks on Primes in Imaginary Quadratic Fields

We generalize the Gaussian moat problem to the finitely many imaginary quadratic fields exhibiting unique factorization in their integers. We map this problem to the Euclidean minimum spanning tree problem and use Delaunay triangulation and Kruskal's algorithm to find moats in these fields in $O(|\mathbf{P}| \log |\mathbf{P}|)$ time, where $\mathbf{P}$ denotes the set of primes we are searching through. Our algorithm uses symmetry and boundaries to correctly and efficiently identify all moats, in order of increasing length, along with the farthest prime reached for each moat, in an underlying unbounded graph of infinite primes. We also derive asymptotic estimates on the density of primes in certain imaginary quadratic fields. Based on this and symmetry arguments, we conjecture that for a given step bound $k$, we can travel farther away from the origin in $\mathbb{Z}[i]$ and $\mathbb{Z}\left[\frac{-1+\sqrt{-3}}{2}\right]$ than in $\mathbb{Z}[\sqrt{-2}]$. This conjecture is corroborated by our computational results.

math.NT↗