Karan Singh

Andrew Li, R. Ravi, Karan Singh et al.

Motivated by the problem of selling large, proprietary data, we consider an information pricing problem proposed by Bergemann et al. that involves a decision-making buyer and a monopolistic seller. The seller has access to the underlying state of the world that determines the utility of the various actions the buyer may take. Since the buyer gains greater utility through better decisions resulting from more accurate assessments of the state, the seller can therefore promise the buyer supplemental information at a price. To contend with the fact that the seller may not be perfectly informed about the buyer's private preferences (or utility), we frame the problem of designing a data product as one where the seller designs a revenue-maximizing menu of statistical experiments. Prior work by Cai et al. showed that an optimal menu can be found in time polynomial in the state space, whereas we observe that the state space is naturally exponential in the dimension of the data. We propose an algorithm which, given only sampling access to the state space, provably generates a near-optimal menu with a number of samples independent of the state space. We then analyze a special case of high-dimensional Gaussian data, showing that (a) it suffices to consider scalar Gaussian experiments, (b) the optimal menu of such experiments can be found efficiently via a semidefinite program, and (c) full surplus extraction occurs if and only if a natural separation condition holds on the set of potential preferences of the buyer.

Udaya Ghai, Karan Singh

The theory of boosting provides a computational framework for aggregating approximate weak learning algorithms, which perform marginally better than a random predictor, into an accurate strong learner. In the realizable case, the success of the boosting approach is underscored by a remarkable fact that the resultant sample complexity matches that of a computationally demanding alternative, namely Empirical Risk Minimization (ERM). This in particular implies that the realizable boosting methodology has the potential to offer computational relief without compromising on sample efficiency. Despite recent progress, in agnostic boosting, where assumptions on the conditional distribution of labels given feature descriptions are absent, ERM outstrips the agnostic boosting methodology in being quadratically more sample efficient than all known agnostic boosting algorithms. In this paper, we make progress on closing this gap, and give a substantially more sample efficient agnostic boosting algorithm than those known, without compromising on the computational (or oracle) complexity. A key feature of our algorithm is that it leverages the ability to reuse samples across multiple rounds of boosting, while guaranteeing a generalization error strictly better than those obtained by blackbox applications of uniform convergence arguments. We also apply our approach to other previously studied learning problems, including boosting for reinforcement learning, and demonstrate improved results.

Rahul Arora, Jiannan Li, Gongyi Shi et al.

Size and distance perception in Virtual Reality (VR) have been widely studied, albeit in a controlled laboratory setting with a small number of participants. We describe a fully remote perceptual study with a gamified protocol to encourage participant engagement, which allowed us to quickly collect high-quality data from a large, diverse participant pool (N=60). Our study aims to understand medium-field size and egocentric distance perception in real-world usage of consumer VR devices. We utilized two perceptual matching tasks -- distance bisection and size matching -- at the same target distances of 1--9 metres. While the bisection protocol indicated a near-universal trend of nonlinear distance compression, the size matching estimates were more equivocal. Varying eye-height from the floor plane showed no significant effect on the judgements. We also discuss the pros and cons of a fully remote perceptual study in VR, the impact of hardware variation, and measures needed to ensure high-quality data.

Udaya Ghai, Holden Lee, Karan Singh et al.

We consider the problem of online prediction in a marginally stable linear dynamical system subject to bounded adversarial or (non-isotropic) stochastic perturbations. This poses two challenges. Firstly, the system is in general unidentifiable, so recent and classical results on parameter recovery do not apply. Secondly, because we allow the system to be marginally stable, the state can grow polynomially with time; this causes standard regret bounds in online convex optimization to be vacuous. In spite of these challenges, we show that the online least-squares algorithm achieves sublinear regret (improvable to polylogarithmic in the stochastic setting), with polynomial dependence on the system's parameters. This requires a refined regret analysis, including a structural lemma showing the current state of the system to be a small linear combination of past states, even if the state grows polynomially. By applying our techniques to learning an autoregressive filter, we also achieve logarithmic regret in the partially observed setting under Gaussian noise, with polynomial dependence on the memory of the associated Kalman filter.

Elad Hazan, Sham M. Kakade, Karan Singh

We consider the problem of controlling an unknown linear dynamical system in the presence of (nonstochastic) adversarial perturbations and adversarial convex loss functions. In contrast to classical control, the a priori determination of an optimal controller here is hindered by the latter's dependence on the yet unknown perturbations and costs. Instead, we measure regret against an optimal linear policy in hindsight, and give the first efficient algorithm that guarantees a sublinear regret bound, scaling as T^{2/3}, in this setting.

Maria Shugrina, Amlan Kar, Karan Singh et al.

We present color sails, a discrete-continuous color gamut representation that extends the color gradient analogy to three dimensions and allows interactive control of the color blending behavior. Our representation models a wide variety of color distributions in a compact manner, and lends itself to applications such as color exploration for graphic design, illustration and similar fields. We propose a Neural Network that can fit a color sail to any image. Then, the user can adjust color sail parameters to change the base colors, their blending behavior and the number of colors, exploring a wide range of options for the original design. In addition, we propose a Deep Learning model that learns to automatically segment an image into color-compatible alpha masks, each equipped with its own color sail. This allows targeted color exploration by either editing their corresponding color sails or using standard software packages. Our model is trained on a custom diverse dataset of art and design. We provide both quantitative evaluations, and a user study, demonstrating the effectiveness of color sail interaction. Interactive demos are available at www.colorsails.com.

Naman Agarwal, Karan Singh

We design differentially private algorithms for the problem of online linear optimization in the full information and bandit settings with optimal $\tilde{O}(\sqrt{T})$ regret bounds. In the full-information setting, our results demonstrate that $ε$-differential privacy may be ensured for free -- in particular, the regret bounds scale as $O(\sqrt{T})+\tilde{O}\left(\frac{1}ε\right)$. For bandit linear optimization, and as a special case, for non-stochastic multi-armed bandits, the proposed algorithm achieves a regret of $\tilde{O}\left(\frac{1}ε\sqrt{T}\right)$, while the previously known best regret bound was $\tilde{O}\left(\frac{1}εT^{\frac{2}{3}}\right)$.