Senior Data Scientist, Boston Consulting Group (BCG X) | PhD (DPhil) Computer Science, University of Oxford
Boston, Massachusetts, United States
Contact Info
557 followers
500+ connections
Experience
Education
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University of Oxford
Doctor of Philosophy - DPhil Computer Science
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Activities and Societies: President of Magdalen College Middle Common Room, President of Computer Science Committee of Graduate Students, Algorithms and Complexity Representative on Joint Consultative Committee of Graduates, Student Chair and Computer Science Representative on Graduate Joint Consultative Forum of Mathematics and Physical/Life Sciences Division
• Oxford-DeepMind Graduate Scholar
• Oxford Computer Science Research Studentship Recipient
• Study tradeoffs between time, memory, and randomness to understand the bounds of computation with a focus on game theoretic problems
• Review academic papers and prove theorems regarding the mathematics behind the foundations of computer science
• Drive towards results that indicate the existence or impossibility of efficient algorithms for certain classes of problems -
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Stanford University
Bachelor of Science - BS Mathematics
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Activities and Societies: Trumpet Section Leader and National Anthem Soloist for Leland Stanford Junior University Marching Band, Trumpet Player, Stanford Wind Symphony, Financial Officer for Stanford University Jewish Student Association, Student Leader for Weekly Religious Services, Volunteer for Stanford University Science in Service, Volunteer Teacher for Stanford Splash
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Sidwell Friends School
High School
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Activities and Societies: Head of Sidwell Friends School Math Team, Player on Sidwell Friends School Tennis Team, Trumpet Player in Sidwell Friends School Jazz Ensemble
Licenses & Certifications
Publications
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PPAD-Complete Pure Approximate Nash Equilibria in Lipschitz Games
International Symposium on Algorithmic Game Theory (SAGT)
Lipschitz games, in which there is a limit λ (the Lipschitz value of the game) on how much a player’s payoffs may change when some other player deviates, were introduced about 10 years ago by Azrieli and Shmaya. They showed via the probabilistic method that n-player Lipschitz games with m strategies per player have pure ϵ-approximate Nash equilibria, for ϵ≥λ\sqrt{8nlog(2mn)}. Here we provide the first hardness result for the corresponding computational problem, showing that even for a simple…
Lipschitz games, in which there is a limit λ (the Lipschitz value of the game) on how much a player’s payoffs may change when some other player deviates, were introduced about 10 years ago by Azrieli and Shmaya. They showed via the probabilistic method that n-player Lipschitz games with m strategies per player have pure ϵ-approximate Nash equilibria, for ϵ≥λ\sqrt{8nlog(2mn)}. Here we provide the first hardness result for the corresponding computational problem, showing that even for a simple class of Lipschitz games (Lipschitz polymatrix games), finding pure ϵ-approximate equilibria is PPAD-complete, for suitable pairs of values (ϵ(n),λ(n)). Novel features of this result include both the proof of PPAD hardness (in which we apply a population game reduction from unrestricted polymatrix games) and the proof of containment in PPAD (by derandomizing the selection of a pure equilibrium from a mixed one). In fact, our approach implies containment in PPAD for any class of Lipschitz games where payoffs from mixed-strategy profiles can be deterministically computed.
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Lower Bounds for the Query Complexity of Equilibria in Lipschitz Games
International Symposium on Algorithmic Game Theory (SAGT)
Nearly a decade ago, Azrieli and Shmaya introduced the class of λ-Lipschitz games in which every player’s payoff function is λ-Lipschitz with respect to the actions of the other players. They showed that such games admit ϵ-approximate pure Nash equilibria for certain settings of ϵ and λ. They left open, however, the question of how hard it is to find such an equilibrium. In this work, we develop a query-efficient reduction from more general games to Lipschitz games. We use this reduction to…
Nearly a decade ago, Azrieli and Shmaya introduced the class of λ-Lipschitz games in which every player’s payoff function is λ-Lipschitz with respect to the actions of the other players. They showed that such games admit ϵ-approximate pure Nash equilibria for certain settings of ϵ and λ. They left open, however, the question of how hard it is to find such an equilibrium. In this work, we develop a query-efficient reduction from more general games to Lipschitz games. We use this reduction to show a query lower bound for any randomized algorithm finding ϵ-approximate pure Nash equilibria of n-player, binary-action, λ-Lipschitz games that is exponential in nλ/ϵ. In addition, we introduce “Multi-Lipschitz games,” a generalization involving player-specific Lipschitz values, and provide a reduction from finding equilibria of these games to finding equilibria of Lipschitz games, showing that the value of interest is the sum of the individual Lipschitz parameters. Finally, we provide an exponential lower bound on the deterministic query complexity of finding ϵ-approximate equilibria of n-player, m-action, λ-Lipschitz games for strong values of ϵ, motivating the consideration of explicitly randomized algorithms in the above results.
Patents
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Machine Learning Based Strength Training System and Apparatus
Filed US 17/382,558
We jointly designed and developed a prototype device to provide form-based feedback on weightlifting exercises using sensors positioned on the barbell and the body. In addition, we constructed a bend-sensitive knee sleeve to detect and analyze technique for strength training and physiotherapy purposes
Other inventors
Honors & Awards
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Bachelor's Degree with Distinction
Stanford University
In recognition of high scholastic attainment, the University awards the Bachelor’s Degree with Distinction. Distinction is awarded to the top 15% of the graduating class based on cumulative grade point averages calculated at the end of Winter Quarter.
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Departmental Honors
Stanford University Department of Mathematics
In recognition of successful completion of special advanced work, departments may recommend their students for honors in the major. Departmental honors programs demand independent creative work at an advanced level in addition to major requirements. Departmental honors programs are not available in every academic department.
Thesis Title: An Exploration of Derandomization and its Relaxations -
Oxford-DeepMind Graduate Scholarship
The University of Oxford
The Oxford Graduate Scholarships were established in 2012 through a ground breaking matched funding initiative. Scholarships are awarded to applicants who have demonstrated excellent academic ability, who will contribute to the University’s ground-breaking research, and who will go on to contribute to the world as leaders in their field, pushing the frontiers of knowledge. The University contributes 40% of the funds for these scholarships, together with 60% from generous donations provided by…
The Oxford Graduate Scholarships were established in 2012 through a ground breaking matched funding initiative. Scholarships are awarded to applicants who have demonstrated excellent academic ability, who will contribute to the University’s ground-breaking research, and who will go on to contribute to the world as leaders in their field, pushing the frontiers of knowledge. The University contributes 40% of the funds for these scholarships, together with 60% from generous donations provided by numerous supporters of the University and its colleges.
DeepMind’s mission is to solve intelligence, combining the best techniques from machine learning and systems neuroscience to build powerful general-purpose learning algorithms. Their generous support has helped the Department of Computer Science continue to attract the world’s most talented scientists in core research themes as well as cross disciplinary areas. -
Studentship for DPhil Computer Science
The University of Oxford Department of Computer Science
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William Lowell Putnam National Math Competition Honor Roll
Mathematical Association of America
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National Merit Scholar
National Merit Scholarship Corporation
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USA Physics Olympiad Semi-Final Exam Honorable Mention
American Association of Physics Teachers
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National AP Scholar
The College Board
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National Finalist, US National Chemistry Olympiad Competition
American Chemical Society
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Certificate of Excellence for Participating in the USA Junior Mathematical Olympiad
Mathematical Association of America
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1st Place in District of Columbia, American Mathematics Contest
Mathematical Association of America
Languages
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English
Native or bilingual proficiency
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