Fast Convergence of Fictitious Play for Diagonal Payoff Matrices

Abernethy, Jacob; Lai, Kevin A.; Wibisono, Andre

doi:10.1137/1.9781611976465.84

Cited by 1 publication

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“…In fact, if Karlin's weak conjecture holds (Karlin, 1962), namely that both players can use FTL to achieve sublinear regret, then neither player must explicitly consider all of their exponentially many strategies! There is some hope that this conjecture is true (see (Abernethy et al, 2021)).…”

Section: F Discussionmentioning

confidence: 95%

“…Nonetheless, it turns out we can approximately solve this game efficiently, in n • poly(d) time! We use a variation on the so-called fictitious play dynamic (Abernethy et al, 2021), in which the hash player performs the multiplicative weights update and the query player chooses the query that minimizes their loss on the hashes played so far (the "Follow-the-Leader" (FTL) approach (Kalai & Vempala, 2005)). Indeed, while the complexity of the game is polynomial in the number of hash player strategies, it is essentially independent of the number of possible queries, as we have reduced the query player's complexity contribution to that of a single minimization (see details in Sec 3.1 and Sec.…”

Section: Technical Description Of Our Algorithmmentioning

confidence: 99%

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Learning to Hash Robustly, Guaranteed

Andoni¹,

Daniel²

2021

Preprint

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The indexing algorithms for the high-dimensional nearest neighbor search (NNS) with the best worst-case guarantees are based on the randomized Locality Sensitive Hashing (LSH), and its derivatives. In practice, many heuristic approaches exist to "learn" the best indexing method in order to speed-up NNS, crucially adapting to the structure of the given dataset. Oftentimes, these heuristics outperform the LSH-based algorithms on real datasets, but, almost always, come at the cost of losing the guarantees of either correctness or robust performance on adversarial queries, or apply to datasets with an assumed extra structure/model. In this paper, we design an NNS algorithm for the Hamming space that has worst-case guarantees essentially matching that of theoretical algorithms, while optimizing the hashing to the structure of the dataset (think instance-optimal algorithms) for performance on the minimum-performing query. We evaluate the algorithm's ability to optimize for a given dataset both theoretically and practically. On the theoretical side, we exhibit a natural setting (dataset model) where our algorithm is much better than the standard theoretical one. On the practical side, we run experiments that show that our algorithm has a 1.8x and 2.1x better recall on the worst-performing queries to the MNIST and ImageNet datasets.Preprint. Under review.

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Section: F Discussionmentioning

confidence: 95%

Section: Technical Description Of Our Algorithmmentioning

confidence: 99%