How much data is sufficient to learn high-performing algorithms? generalization guarantees for data-driven algorithm design

Balcan, Maria-Florina; DeBlasio, Dan; Dick, Travis; Kingsford, Carl; Sandholm, Tüomas; Vitercik, Ellen

doi:10.1145/3406325.3451036

Cited by 21 publications

(44 citation statements)

References 39 publications

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“…In Lemma 3.4 and Theorem 3.5 we showed that there are O(W 2 W α+2 W β+nW ) multivariate polynomials that belong to a family of polynomials G with VCdim(G * ) ≤ 1 + mW (G * denotes the dual of G) that partition C into regions such that resulting sequence of cuts is invariant in each region. By Claim 3.5 by Balcan et al [9], the number of regions is…”

Section: Learning Cut Selection Policiesmentioning

confidence: 81%

“…Our main result in this section is a proof that the dual functions are well-structured (Lemma 3.2), which then allows us to apply a result by Balcan et al [9] to bound Pdim({f u : u ∈ [0, 1] m }) (Theorem 3.3). Proving that the dual functions are well-structured is challenging because they are volatile: slightly perturbing u can cause the tree size to shift from constant to exponential in n, as we prove in the following theorem.…”

Section: Learning a Single Cutmentioning

confidence: 94%

“…These O(r 2 ) hyperplanes partition R d into regions such that as µ varies in a given region, the cut chosen from C is invariant. The desired pseudo-dimension bound follows from the main result of Balcan et al [9]. Theorem 4.1 can be directly instantiated with the class of CG cuts.…”

Section: Learning Cut Selection Policiesmentioning

confidence: 99%

“…The term that collects a coefficient of a i [j] is precisely u w [m + ] times the sum of all terms from the first cuts with a coefficient of a i [j]. Using standard facts about the VC dimension of vector spaces and their duals in conjunction with Lemma 3.4 and the framework of Balcan et al [9] yields the theorem statement.…”

Section: Learning a Sequence Of Cutsmentioning

confidence: 99%

“…This insight allows us to better understand tree size as a function of the parameters. We then leverage results by Balcan et al [9] that show how to use structure exhibited by dual functions (measuring an algorithm's performance, such as its tree size, as a function of its parameters) to derive sample complexity bounds.…”

Section: Summary Of Main Contributions and Overview Of Techniquesmentioning

confidence: 99%

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Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond

Balcan,

Prasad,

Sandholm

et al. 2021

Preprint

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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.

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Section: Learning Cut Selection Policiesmentioning

confidence: 81%

Section: Learning a Single Cutmentioning

confidence: 94%

Section: Learning Cut Selection Policiesmentioning

confidence: 99%

Section: Learning a Sequence Of Cutsmentioning

confidence: 99%

Section: Summary Of Main Contributions and Overview Of Techniquesmentioning

confidence: 99%

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Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond

Balcan,

Prasad,

Sandholm

et al. 2021

Preprint

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Learn to optimize—a brief overview

Tang,

Yao

2024

National Science Review

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Most optimization problems of practical significance are typically solved by highly configurable parameterized algorithms. To achieve the best performance on a problem instance, a trial-and-error configuration process is required, which is very costly and even prohibitive for problems that are already computationally intensive, e.g., optimization problems associated with machine learning tasks. In the past decades, many studies have been conducted to accelerate the tedious configuration process by learning from a set of training instances. This article refers these studies as Learn to Optimize and reviews the progress achieved.

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Adaptive, sample-specific parameter selection for more accurate transcript assembly

Shen,

Yan,

Kingsford

2024

Preprint

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Transcript assemblers are tools to reconstruct expressed transcripts from RNA-seq data. These tools have a large number of tunable parameters, and accurate transcript assembly requires setting them suitably. Because of the heterogeneity of different RNA-seq samples, a single default setting or a small fixed set of parameter candidates can only support the good performance of transcript assembly on average, but are often suboptimal for many individual samples. Manually tuning parameters for each sample is time consuming and requires specialized experience. Therefore, developing an automated system that can advise good parameter settings for individual samples becomes an important problem. Using Bayesian optimization and contrastive learning, we develop a new automated parameter advising system for transcript assembly that can generate sets of sample-specific good parameter candidates. Our framework achieves efficient sample-specific parameter advising by learning parameter knowledge from a representative set of existing RNA-seq samples and transferring the knowledge to unseen samples. We use Scallop and StringTie, two well-known transcript assemblers, to test our framework on two collections of RNA-seq samples. Results show that our new parameter advising system significantly outperforms the previous advising method in each dataset and each transcript assembler. Scripts to reproduce the results from this study can be found at https://github.com/Kingsford-Group/autoparadvisor.

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How much data is sufficient to learn high-performing algorithms? generalization guarantees for data-driven algorithm design

Cited by 21 publications

References 39 publications

Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond

Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond

Learn to optimize—a brief overview

Adaptive, sample-specific parameter selection for more accurate transcript assembly

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