The classical foundations of optimization were built for a world that no longer exists: clean data, fixed objectives, and static computational models. Modern decision systems violate each of these assumptions. Data is noisy, biased, and heterogeneous; objectives are contested across stakeholders and increasingly expressed through human interaction and language; and computation itself is evolving through machine learning systems, specialized hardware, and quantum architectures. My research develops new mathematical foundations for optimization to address these challenges, while carrying these ideas back into the institutions and systems that motivate them. My work has informed or been deployed in settings spanning hiring platforms, public school admissions, organ allocation, electric utility systems, districting and emergency response, AI infrastructure, and quantum hardware benchmarking. The three broad thrusts we are currently focused on are:

(1) Contextual and Noisy Data. Algorithms for optimization and learning under systematically biased, noisy, or partially ordered information, with applications in hiring, admissions, recommendation systems, rankings, and healthcare.

(2) Portfolios for Underspecified Formulations. Optimization frameworks that compute provably small sets of solutions spanning stakeholder trade-offs and welfare frontiers, with applications in facility location, reinforcement learning, LLM alignment, and equitable infrastructure planning.

(3) Optimization under Heterogeneous Computation. Optimization methods that compose classical subroutines, learned modules, and hardware-specific compute — including near-term quantum devices — each with its own cost, fidelity, and noise profile.

Underlying these directions is a parallel body of my work on the foundations of optimization, including constrained descent methods, submodular optimization, online optimization, and approximation algorithms.

1. Contextual and Noisy Data. Classical online and offline optimization assumes input data is an unbiased estimate of an underlying truth. When data is systematically biased, partially ordered, or arrives from heterogeneous sources, classical algorithms not only lose their guarantees — they amplify the very distortions in the data. My group develops new algorithms that retain provable guarantees under noisy and imperfect data, and translates them into deployed systems in hiring, admissions, healthcare, and rankings.
[For more details, check out this page. ]

Here are some selected publications in this thread:

  • Adaptive Cost-Aware Stochastic Optimization with Heterogeneous Gradient Oracles — with T. Li. Working paper.
  • Learning Customer Value from Heterogeneous Signals: A Bandit Approach for Mixed Fidelity Learning with Costs — with D. Duval, M. Pollack. Working paper.
  • Improving Clinical Decision Support through Interpretable Machine Learning and Error Correction in Electronic Health Records – with M. Arora, H. Mortagy, N. Dwarshius, J. Wang, P. Yang, A. Holder, R. Kamaleswaran, Journal of the American Medical Informatics Association (JAMIA) 2025.
  • Secretary Problems with Biased Evaluations using Partial Ordinal Information – with J. Salem. Management Science 2023.
  • Discovering Opportunities in New York City’s Discovery Program: an Analysis of Affirmative Action Mechanisms – with Y. Faenza, X. Zhang, EC 2023 (major rev, Operations Research). arxiv
  • Reducing the Filtering Effect in Public School Admissions: A Bias-aware Analysis for Targeted Interventions – with Y. Faenza, A. Vuorinen, X. Zhang, ACDA 2023 (minor rev, at M&SOM) arxiv
  • Using Algorithms to Tame Discrimination – with D. Desai, J. Salem, UC Davis Law Review, 2023.
  • Don’t let Ricci v. DeStefano Hold You Back: A Bias-Aware Legal Solution to the Hiring Paradox – with J. Salem, D. Desai, ACM FAccT 2022
  • Closing the GAP: Mitigating Bias in Online Resume-Filtering, with J. Salem. WINE 2020. link

2. Portfolios for Underspecified Formulations. When objectives are contested across stakeholders, under-specified, or expressed through language and human interaction, classical multi-objective optimization gives the wrong output — either a single scalarized point (assuming weights are known) or an exponentially large Pareto frontier. My group establishes that the right output is a provably small portfolio of solutions whose welfare guarantees jointly cover the entire frontier within a constant factor. The framework now spans facility location, multi-objective reinforcement learning, LLM alignment, and equitable infrastructure planning.
For more details, check out this page.

Here are some selected publications in this thread:

Portfolio of Small Set of Solutions:

  • Many Preferences, Few Policies: Towards Scalable Language Model Personalization – with Kim, Moondra, Nahavandi, Perrault, Tambe. Under submission (arxiv)
  • Improved Regret Guarantees for Online Mirror Descent using a Portfolio of Mirror Maps – with J. Moondra, M. Singh. Under submission (arxiv)
  • Navigating the Social Welfare Frontier: Portfolios for Multi-objective Reinforcement Learning, with C. Kim, J. Moondra, S. Verma, M. Pollack, L. Kong, M. Tambe, ICML 2025.
  • Balancing Notions of Equity: Trade-offs Between Fair Portfolio Sizes and Achievable Guarantees – with J. Moondra, M. Singh, SODA 2025. Minor rev, Mathematical Programming, 2025.
  • Too many fairness metrics: Is there a solution? – with A. Jalan, G. Ranade, H. Yang, S. Zhuang, Fields Institute Communication Series 2025.
  • Which Lp norm is the fairest? Approximations for fair facility location across all “p” – with J. Moondra, M. Singh. EC 2023.

Multi-Criteria Guarantees with a Single Solution or Algorithm:

  • Algorithmic Challenges in Ensuring Fairness at the Time of Decision – with J. Salem, V. Kamble, WINE 2022, and Operations Research 2025.
  • Fair and Reliable Reconnections for Temporary Disruptions in Electric Distribution Networks – with C. Hettle and D. Molzahn, INFORMS Journal on Computing 2025.
  • Equitably allocating wildfire resilience investments for power grids: The curse of aggregation and vulnerability indices – with M. Pollack, R. Piansky, D. Molzahn, Applied Energy, 2025.
  • Temporal Fairness in Online Decision-Making, Swati Gupta, Jad Salem, Vijay Kamble, Book Chapter in Ethics in Artificial Intelligence: Bias, Fairness and Beyond, 2023.
  • Individual Fairness in Hindsight – with V. Kamble, Journal of Machine Learning Research 2021.
  • Balanced Districting on Grid Graphs with Provable Compactness and Contiguity – with
    C. Hettle, S. Zhu, Y. Xie, FORC 2021.
  • Group-Fair Online Allocation in Continuous Time – with S. Cayci, A. Eryilmaz, NeurIPS 2020.

3. Optimization under Heterogeneous Computation: Modern solvers no longer rely on a single deterministic oracle. They compose classical algorithmic subroutines, learned ML modules, and hardware-specific compute — including near-term quantum devices — each with its own cost, fidelity, and noise profile. My group develops the mathematical foundations of optimization in this regime.
For more details, check out this page.

Here are some selected publications in this thread:

Optimization for Near-Term Quantum Devices:

  • Comparison of Hyperplane Rounding for Max-Cut and Quantum Approximate Optimization Algorithm over Certain Regular Graph Families – with R. Tate. Operations Research Letters, 2026.
  • Promise of Graph Sparsification and Decomposition for Noise Reduction in QAOA: Analysis for Trapped-Ion Compilations – with J. Moondra, G. Mohler, P. Lotshaw. Revise and Resubmit, Quantum 2025.
  • Strategies for running the QAOA at hundreds of qubits – with B. Augustino, M. Cain, E. Farhi, S. Gutmann, B. Ranard, E. Tang and K. Van Kirk, 2025.
  • Quantum Optimization: Potential, Challenges, and the Path Forward – with 40+ authors, Nature Reviews Physics 2024
  • Classically-inspired Mixers for QAOA Beat Goemans-Williamson’s Max-Cut at Low Circuit Depths, with R. Tate, J. Moondra, B. Gard, G. Mohler Quantum 2023
  • Generating Target Graph Couplings for QAOA from Native Quantum Hardware Couplings with J. Rajakumar, J. Moondra and C. Herold, Physical Review A, 2022
  • Bridging Classical and Quantum using SDP initialized warm-starts for QAOA with R. Tate, M. Farhadi, C. Herold and G. Mohler ACM Transactions of Quantum Computing, 2022

Optimization for Modern Data Centers:

  • TACOS: Topology-Aware Collective Algorithm Synthesizer for Distributed Machine Learning — with W. Won, M. Elavazhagan, S. Srinivasan, A. Durg, S. Kaul, T. Krishna. MICRO 2024.

Algorithmic Foundations Underlying These Programs

These three programs rest on a parallel body of structural and algorithmic results my group has developed on the foundations of structured optimization. These results are not application-driven — they are the algorithmic engine room that makes the deployed work above tractable.

  • Faster Parametric Submodular Function Minimization using Duality – with Zhu. Under submission.(arxiv)
  • Hardness and Approximation of Submodular Minimum Linear Ordering Problems, with M. Farhadi, S. Sun, P. Tetali, M. Wigal Mathematical Programming 2023.
  • Electrical Flows over Spanning Trees with A. Khodabhaksh, H. Mortagy, E. Nikolova Mathematical Programming B, 2022.
  • Reusing Combinatorial Structure: Faster Iterative Projections over Submodular Base Polytopes with J. Moondra, H. Mortagy NeurIPS 2021.
  • Walking in the Shadow: A New Perspective on Descent Directions for Constrained Minimization with H. Mortagy, S. Pokutta, NeurIPS 2020, (major rev) Mathematics of Operations Research.
  • Limited Memory Kelley’s Method Converges for Composite Convex and Submodular Objectives with M. Udell, S. Zhou NeurIPS 2018 (spotlight)
  • What works best when? A Framework for Systematic Heuristic Evaluation with J. Silberholz, I. Dunning, INFORMS Journal on Computing, 2018
  • A 4/3 approximation for TSP on cubic 3-edge-connected graph with N. Agarwal, N. Garg, Operations Research Letters, 2018
  • Newton’s Method for Parametric Submodular Function Minimization with M. Goemans, P. Jaillet, IPCO 2017