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Documents authored by Bhaskara, Aditya

Document
DOI: 10.4230/LIPIcs.ITCS.2023.16
Online Learning and Bandits with Queried Hints

Authors: Aditya Bhaskara, Sreenivas Gollapudi, Sungjin Im, Kostas Kollias, and Kamesh Munagala

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
We consider the classic online learning and stochastic multi-armed bandit (MAB) problems, when at each step, the online policy can probe and find out which of a small number (k) of choices has better reward (or loss) before making its choice. In this model, we derive algorithms whose regret bounds have exponentially better dependence on the time horizon compared to the classic regret bounds. In particular, we show that probing with k = 2 suffices to achieve time-independent regret bounds for online linear and convex optimization. The same number of probes improve the regret bound of stochastic MAB with independent arms from O(√{nT}) to O(n² log T), where n is the number of arms and T is the horizon length. For stochastic MAB, we also consider a stronger model where a probe reveals the reward values of the probed arms, and show that in this case, k = 3 probes suffice to achieve parameter-independent constant regret, O(n²). Such regret bounds cannot be achieved even with full feedback after the play, showcasing the power of limited "advice" via probing before making the play. We also present extensions to the setting where the hints can be imperfect, and to the case of stochastic MAB where the rewards of the arms can be correlated.
Cite as

Aditya Bhaskara, Sreenivas Gollapudi, Sungjin Im, Kostas Kollias, and Kamesh Munagala. Online Learning and Bandits with Queried Hints. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 16:1-16:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bhaskara_et_al:LIPIcs.ITCS.2023.16,
  author =	{Bhaskara, Aditya and Gollapudi, Sreenivas and Im, Sungjin and Kollias, Kostas and Munagala, Kamesh},
  title =	{{Online Learning and Bandits with Queried Hints}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{16:1--16:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.16},
  URN =		{urn:nbn:de:0030-drops-175197},
  doi =		{10.4230/LIPIcs.ITCS.2023.16},
  annote =	{Keywords: Online learning, multi-armed bandits, regret}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.4
Low Rank Approximation in the Presence of Outliers

Authors: Aditya Bhaskara and Srivatsan Kumar

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
We consider the problem of principal component analysis (PCA) in the presence of outliers. Given a matrix A (d x n) and parameters k, m, the goal is to remove a set of at most m columns of A (outliers), so as to minimize the rank-k approximation error of the remaining matrix (inliers). While much of the work on this problem has focused on recovery of the rank-k subspace under assumptions on the inliers and outliers, we focus on the approximation problem. Our main result shows that sampling-based methods developed in the outlier-free case give non-trivial guarantees even in the presence of outliers. Using this insight, we develop a simple algorithm that has bi-criteria guarantees. Further, unlike similar formulations for clustering, we show that bi-criteria guarantees are unavoidable for the problem, under appropriate complexity assumptions.
Cite as

Aditya Bhaskara and Srivatsan Kumar. Low Rank Approximation in the Presence of Outliers. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bhaskara_et_al:LIPIcs.APPROX-RANDOM.2018.4,
  author =	{Bhaskara, Aditya and Kumar, Srivatsan},
  title =	{{Low Rank Approximation in the Presence of Outliers}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.4},
  URN =		{urn:nbn:de:0030-drops-94087},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.4},
  annote =	{Keywords: Low rank approximation, PCA, Robustness to outliers}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.16
Sublinear Algorithms for MAXCUT and Correlation Clustering

Authors: Aditya Bhaskara, Samira Daruki, and Suresh Venkatasubramanian

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We study sublinear algorithms for two fundamental graph problems, MAXCUT and correlation clustering. Our focus is on constructing core-sets as well as developing streaming algorithms for these problems. Constant space algorithms are known for dense graphs for these problems, while Omega(n) lower bounds exist (in the streaming setting) for sparse graphs. Our goal in this paper is to bridge the gap between these extremes. Our first result is to construct core-sets of size O~(n^{1-delta}) for both the problems, on graphs with average degree n^{delta} (for any delta >0). This turns out to be optimal, under the exponential time hypothesis (ETH). Our core-set analysis is based on studying random-induced sub-problems of optimization problems. To the best of our knowledge, all the known results in our parameter range rely crucially on near-regularity assumptions. We avoid these by using a biased sampling approach, which we analyze using recent results on concentration of quadratic functions. We then show that our construction yields a 2-pass streaming (1+epsilon)-approximation for both problems; the algorithm uses O~(n^{1-delta}) space, for graphs of average degree n^delta.
Cite as

Aditya Bhaskara, Samira Daruki, and Suresh Venkatasubramanian. Sublinear Algorithms for MAXCUT and Correlation Clustering. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bhaskara_et_al:LIPIcs.ICALP.2018.16,
  author =	{Bhaskara, Aditya and Daruki, Samira and Venkatasubramanian, Suresh},
  title =	{{Sublinear Algorithms for MAXCUT and Correlation Clustering}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{16:1--16:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.16},
  URN =		{urn:nbn:de:0030-drops-90203},
  doi =		{10.4230/LIPIcs.ICALP.2018.16},
  annote =	{Keywords: Sublinear algorithms, Streaming algorithms, Core-sets, Maximum cut, Correlation clustering}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.7
Non-Negative Sparse Regression and Column Subset Selection with L1 Error

Authors: Aditya Bhaskara and Silvio Lattanzi

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
We consider the problems of sparse regression and column subset selection under L1 error. For both problems, we show that in the non-negative setting it is possible to obtain tight and efficient approximations, without any additional structural assumptions (such as restricted isometry, incoherence, expansion, etc.). For sparse regression, given a matrix A and a vector b with non-negative entries, we give an efficient algorithm to output a vector x of sparsity O(k), for which |Ax - b|_1 is comparable to the smallest error possible using non-negative k-sparse x. We then use this technique to obtain our main result: an efficient algorithm for column subset selection under L1 error for non-negative matrices.
Cite as

Aditya Bhaskara and Silvio Lattanzi. Non-Negative Sparse Regression and Column Subset Selection with L1 Error. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bhaskara_et_al:LIPIcs.ITCS.2018.7,
  author =	{Bhaskara, Aditya and Lattanzi, Silvio},
  title =	{{Non-Negative Sparse Regression and Column Subset Selection with L1 Error}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.7},
  URN =		{urn:nbn:de:0030-drops-83548},
  doi =		{10.4230/LIPIcs.ITCS.2018.7},
  annote =	{Keywords: Sparse regression, L1 error optimization, Column subset selection}
}
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