[Theory] Re: [Theory Lunch] Mohammad Reza Aminian

[Aaron Potechin via Theory]

Hi everyone,


As Alec said yesterday, there will be an additional theory talk tomorrow at noon in JCL 390. Yassine Ghannane, who is visiting this week, will present his work on polynomial calculus over non-Boolean bases.


After Yassine's talk, we will go out for lunch (which Sasha Razborov generously agreed to cover).


Best,

Aaron


Title : Polynomial calculus over non-Boolean bases


Abstract : In a recent breakthrough, Sokolov [Sok'20] proved the first lower bounds for polynomial calculus over the {± 1} basis, which were then extended to finite domains over finite fields [IMP'23, DMM'24]. We further extend the landscape of our understanding of polynomial calculus over non-Boolean bases in several directions :


1)FPHP over {± 1}: We prove exponential size lower bounds for the functional pigeonhole principle over the {± 1} basis, answering an open problem posed in [Sok'20].


2)Coloring over roots of unity : We extend the recent average-case hardness result for coloring [CdRN+23] to the roots of unity encoding by proving exponential size lower bounds in this setting.


3)Automatability : We show size non-automatability of polynomial calculus over {0,1} and {± 1} variables simultaneously.


4)Polynomial calculus over {1,2} : We show that polynomial calculus over R with domain {a,b}, when a/b is not a root of unity, can be surprisingly powerful : it can polynomially simulate bounded coefficient cutting planes.

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From: Theory <theory-bounces at mailman.cs.uchicago.edu> on behalf of Alec Sun via Theory <theory at mailman.cs.uchicago.edu>
Sent: Tuesday, May 6, 2025 11:23 AM
To: theory at mailman.cs.uchicago.edu <theory at mailman.cs.uchicago.edu>; Aminian, Mohammad Reza <MAminian at chicagobooth.edu>
Subject: [Theory] [Theory Lunch] Mohammad Reza Aminian

Please join us for the seventh theory lunch of the quarter tomorrow!

Time: Wednesday, May 7, 2025, 12pm-1pm in JCL 390

Speaker: Mohammad Reza Aminian

Title: Stationary Online Contention Resolution Schemes

Abstract: [See attachment]

On Mon, Apr 28, 2025 at 4:36 PM Alec Sun <alecsun at uchicago.edu<mailto:alecsun at uchicago.edu>> wrote:
Please join us for the sixth theory lunch of the quarter tomorrow. Note the change in day of the week, time, and location just for this week!

Time: Tuesday, April 29, 2025, 12:30pm-1:30pm in JCL 298

Speaker: Aditya Prasad

Title: Supermodular Combinatorial Contracts

Abstract: We present combinatorial contracts in the single-agent combinatorial action model of [Duetting, Ezra, Feldman, Kesselheim, FOCS 2021] and the multi-agent model of [Duetting, Ezra, Feldman, Kesselheim, STOC 2023]. For the single-agent combinatorial action setting, we give a poly-time algorithm for finding the optimal contract, provided that the agent’s demand problem can be solved efficiently and there are poly-many breakpoints in the agent’s demand. This implies an efficient algorithm for supermodular rewards. For the multi-agent setting, our focus is on settings with supermodular rewards. We give an additive PTAS for a natural class of graph-based rewards when the agents have identical costs, and show that even in this special case it’s NP-hard to obtain any finite multiplicative approximation, or an additive FPTAS.

Note: Theory lunch will return to its normal time on Wednesday 12pm for the rest of the quarter.

On Tue, Apr 22, 2025 at 12:51 PM Alec Sun <alecsun at uchicago.edu<mailto:alecsun at uchicago.edu>> wrote:
Please join us for the fifth theory lunch of the quarter tomorrow!

Time: Wednesday, April 23, 2025, 12pm-1pm in JCL 390

Speaker: Yifan Wu

Title: Calibration Error for Decision Making

Abstract: Calibration allows predictions to be reliably interpreted as probabilities by decision makers. We propose a decision-theoretic calibration error, the Calibration Decision Loss (CDL), defined as the maximum improvement in decision payoff obtained by calibrating the predictions, where the maximum is over all payoff-bounded decision tasks. Vanishing CDL guarantees the payoff loss from miscalibration vanishes simultaneously for all downstream decision tasks. We show separations between CDL and existing calibration error metrics, including the most well-studied metric Expected Calibration Error (ECE). Our main technical contribution is a new efficient algorithm for online calibration that achieves near-optimal O(logT / \sqrt{T}) expected CDL, bypassing the Ω(T^{−0.472}) lower bound for ECE by Qiao and Valiant (2021).

Note: Next week JCL 390 and 298 are used for other events on Wednesday, so theory lunch will happen on Tuesday, April 29, 2025, 12pm-1pm in JCL 298.

On Wed, Apr 16, 2025 at 11:15 AM Alec Sun <alecsun at uchicago.edu<mailto:alecsun at uchicago.edu>> wrote:
Please join us for the fourth theory lunch of the quarter today!

Time: Wednesday, April 16, 2025, 12pm-1pm in JCL 390

Speaker: Andrzej Kaczmarczyk

Title: Learning Real-Life Approval Elections

Abstract: We study how to learn an approval election, i.e., an election in which each voter selects which candidates they approve. Specifically, we focus on the independent approval model (IAM), where each candidate has its own approval probability and is approved independently of the other ones. We propose algorithms for learning IAMs and their mixtures from data, using either maximum likelihood estimation or Bayesian learning. We then apply these algorithms to a large set of real-life elections. In particular, we find that single-component models are rarely sufficient to capture the complexity of real-life data, whereas their mixtures perform well.

On Wed, Apr 16, 2025 at 11:01 AM Alec Sun <alecsun at uchicago.edu<mailto:alecsun at uchicago.edu>> wrote:
Please join us for the fourth theory lunch of the quarter today!

Time: Wednesday, April 16, 2025, 12pm-1pm in JCL 390

Speaker: Andrzej Kaczmarczyk

Title: Learning Real-Life Approval Elections

Abstract: We study how to learn an approval election, i.e., an election in which each voter selects which candidates they approve. Specifically, we focus on the independent approval model (IAM), where each candidate has its own approval probability and is approved independently of the other ones. We propose algorithms for learning IAMs and their mixtures from data, using either maximum likelihood estimation or Bayesian learning. We then apply these algorithms to a large set of real-life elections. In particular, we find that single-component models are rarely sufficient to capture the complexity of real-life data, whereas their mixtures perform well.

On Tue, Apr 8, 2025 at 1:05 PM Alec Sun <alecsun at uchicago.edu<mailto:alecsun at uchicago.edu>> wrote:
Please join us for the third theory lunch of the quarter tomorrow!

Time: Wednesday, April 9, 2025, 12pm-1pm in JCL 390

Speaker: Subhodh Kotekal

Title: Variance estimation in compound decision theory under boundedness

Abstract: The normal means model is often studied under the assumption of a known variance. However, ignorance of the variance is a frequent issue in applications and basic theoretical questions still remain open in this setting. This article establishes that the sharp minimax rate of variance estimation in square error is $(\log\log n/\log n)^2$ under arguably the most mild assumption imposed for identifiability: bounded means. The rate-optimal estimator proposed in this article achieves the optimal rate by estimating $O\left(\log n/\log\log n\right)$ cumulants and leveraging a variational representation of the noise variance in terms of the cumulants of the data distribution. The minimax lower bound involves a moment matching construction.

On Tue, Apr 1, 2025 at 1:38 PM Alec Sun <alecsun at uchicago.edu<mailto:alecsun at uchicago.edu>> wrote:
Please join us for the second theory lunch of the quarter tomorrow!

Time: Wednesday, April 2, 2025, 12pm-1pm in JCL 390

Speaker: Dravy Sharma

Title: Provable tuning of deep learning model hyperparameters

Abstract: Modern machine learning algorithms, especially deep learning-based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian optimization and random search-based approaches to automating this laborious and compute-intensive task, the fundamental learning-theoretic complexity of tuning hyperparameters for deep neural networks is poorly understood. Inspired by this glaring gap, we initiate the formal study of hyperparameter tuning complexity in deep learning under a powerful data-driven paradigm. A major difficulty is that the utility function as a function of the hyperparameter is very volatile and furthermore, it is given implicitly by an optimization problem over the model parameters. To tackle this challenge, we employ subtle concepts from differential/algebraic geometry and constrained optimization to show that the learning-theoretic complexity of the corresponding family of utility functions is bounded. We instantiate our results and provide sample complexity bounds for concrete applications—tuning a hyperparameter that interpolates neural activation functions and setting the kernel parameter in graph neural networks. The talk is based on joint work with Nina Balcan and Anh Nguyen.

On Tue, Mar 25, 2025, 4:52 PM Alec Sun <alecsun at uchicago.edu<mailto:alecsun at uchicago.edu>> wrote:
Please join us for the first theory lunch of the quarter tomorrow!

Time: Wednesday, March 26, 2025, 12pm-1pm in JCL 390

Speaker: Olga Medrano

Title: Short Visit to Regularity Lemmas

Abstract: In this expository talk, we will overview Szémerédi’s regularity lemma, a result from extremal graph theory with different applications. We will then mention some considerations about this result, including the existence of irregular pairs in the partitions obtained, as well as the large size of those partitions. Time permitting, we very briefly reflect on how the proof of Szémerédi's regularity lemma is not algorithmic and mention a few lines of work that were focused on finding algorithms to output regular partitions. In the second half of this talk, we will describe versions of this lemma over certain classes of graphs. In particular, we state both the Ultra-strong regularity lemma, which works for the class of graphs of bounded VC dimension, and the Stable regularity lemma, which works for the class of k-edge stable graphs (namely, those not containing a bi-induced bipartite graph). We conclude by acknowledging that algorithmic questions for both results remain open.
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