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Andres Munoz

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4 papers

1 author row

NeurIPS Conference 2019 Conference Paper

Differentially Private Covariance Estimation

Kareem Amin
Travis Dick
Alex Kulesza
Andres Munoz
Sergei Vassilvitskii

The covariance matrix of a dataset is a fundamental statistic that can be used for calculating optimum regression weights as well as in many other learning and data analysis settings. For datasets containing private user information, we often want to estimate the covariance matrix in a way that preserves differential privacy. While there are known methods for privately computing the covariance matrix, they all have one of two major shortcomings. Some, like the Gaussian mechanism, only guarantee (epsilon, delta)-differential privacy, leaving a non-trivial probability of privacy failure. Others give strong epsilon-differential privacy guarantees, but are impractical, requiring complicated sampling schemes, and tend to perform poorly on real data. In this work we propose a new epsilon-differentially private algorithm for computing the covariance matrix of a dataset that addresses both of these limitations. We show that it has lower error than existing state-of-the-art approaches, both analytically and empirically. In addition, the algorithm is significantly less complicated than other methods and can be efficiently implemented with rejection sampling.

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NeurIPS Conference 2017 Conference Paper

Revenue Optimization with Approximate Bid Predictions

Andres Munoz
Sergei Vassilvitskii

In the context of advertising auctions, finding good reserve prices is a notoriously challenging learning problem. This is due to the heterogeneity of ad opportunity types, and the non-convexity of the objective function. In this work, we show how to reduce reserve price optimization to the standard setting of prediction under squared loss, a well understood problem in the learning community. We further bound the gap between the expected bid and revenue in terms of the average loss of the predictor. This is the first result that formally relates the revenue gained to the quality of a standard machine learned model.

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NeurIPS Conference 2015 Conference Paper

Revenue Optimization against Strategic Buyers

Mehryar Mohri
Andres Munoz

We present a revenue optimization algorithm for posted-price auctions when facing a buyer with random valuations who seeks to optimize his $\gamma$-discounted surplus. To analyze this problem, we introduce the notion of epsilon-strategic buyer, a more natural notion of strategic behavior than what has been used in the past. We improve upon the previous state-of-the-art and achieve an optimal regret bound in $O\Big( \log T + \frac{1}{\log(1/\gamma)} \Big)$ when the seller can offer prices from a finite set $\cP$ and provide a regret bound in $\widetilde O \Big(\sqrt{T} + \frac{T^{1/4}}{\log(1/\gamma)} \Big)$ when the buyer is offered prices from the interval $[0, 1]$.

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NeurIPS Conference 2014 Conference Paper

Optimal Regret Minimization in Posted-Price Auctions with Strategic Buyers

Mehryar Mohri
Andres Munoz

We study revenue optimization learning algorithms for posted-price auctions with strategic buyers. We analyze a very broad family of monotone regret minimization algorithms for this problem, which includes the previous best known algorithm, and show that no algorithm in that family admits a strategic regret more favorable than $\Omega(\sqrt{T})$. We then introduce a new algorithm that achieves a strategic regret differing from the lower bound only by a factor in $O(\log T)$, an exponential improvement upon the previous best algorithm. Our new algorithm admits a natural analysis and simpler proofs, and the ideas behind its design are general. We also report the results of empirical evaluations comparing our algorithm with the previous best algorithm and show a consistent exponential improvement in several different scenarios.

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