Garud Iyengar

Necdet Serhat Aybat, Garud Iyengar

We propose a first-order augmented Lagrangian algorithm (FAL) for solving the basis pursuit problem. FAL computes a solution to this problem by inexactly solving a sequence of L1-regularized least squares sub-problems. These sub-problems are solved using an infinite memory proximal gradient algorithm wherein each update reduces to "shrinkage" or constrained "shrinkage". We show that FAL converges to an optimal solution of the basis pursuit problem whenever the solution is unique, which is the case with very high probability for compressed sensing problems. We construct a parameter sequence such that the corresponding FAL iterates are eps-feasible and eps-optimal for all eps>0 within O(log(1/eps)) FAL iterations. Moreover, FAL requires at most O(1/eps) matrix-vector multiplications of the form Ax or A^Ty to compute an eps-feasible, eps-optimal solution. We show that FAL can be easily extended to solve the basis pursuit denoising problem when there is a non-trivial level of noise on the measurements. We report the results of numerical experiments comparing FAL with the state-of-the-art algorithms for both noisy and noiseless compressed sensing problems. A striking property of FAL that we observed in the numerical experiments with randomly generated instances when there is no measurement noise was that FAL always correctly identifies the support of the target signal without any thresholding or post-processing, for moderately small error tolerance values.

Wonyoung Kim, Garud Iyengar, Assaf Zeevi

We propose a new regret minimization algorithm for episodic sparse linear Markov decision process (SMDP) where the state-transition distribution is a linear function of observed features. The only previously known algorithm for SMDP requires the knowledge of the sparsity parameter and oracle access to an unknown policy. We overcome these limitations by combining the doubly robust method that allows one to use feature vectors of \emph{all} actions with a novel analysis technique that enables the algorithm to use data from all periods in all episodes. The regret of the proposed algorithm is $\tilde{O}(σ^{-1}_{\min} s_{\star} H \sqrt{N})$, where $σ_{\min}$ denotes the restrictive the minimum eigenvalue of the average Gram matrix of feature vectors, $s_\star$ is the sparsity parameter, $H$ is the length of an episode, and $N$ is the number of rounds. We provide a lower regret bound that matches the upper bound up to logarithmic factors on a newly identified subclass of SMDPs. Our numerical experiments support our theoretical results and demonstrate the superior performance of our algorithm.

Wonyoung Kim, Garud Iyengar, Assaf Zeevi

We consider the linear contextual multi-class multi-period packing problem (LMMP) where the goal is to pack items such that the total vector of consumption is below a given budget vector and the total value is as large as possible. We consider the setting where the reward and the consumption vector associated with each action is a class-dependent linear function of the context, and the decision-maker receives bandit feedback. LMMP includes linear contextual bandits with knapsacks and online revenue management as special cases. We establish a new estimator which guarantees a faster convergence rate, and consequently, a lower regret in such problems. We propose a bandit policy that is a closed-form function of said estimated parameters. When the contexts are non-degenerate, the regret of the proposed policy is sublinear in the context dimension, the number of classes, and the time horizon $T$ when the budget grows at least as $\sqrt{T}$. We also resolve an open problem posed by Agrawal & Devanur (2016) and extend the result to a multi-class setting. Our numerical experiments clearly demonstrate that the performance of our policy is superior to other benchmarks in the literature.

Wonyoung Kim, Min-Hwan Oh, Garud Iyengar et al.

Reinforcement learning with multinomial logistic (MNL) function approximation has become an important framework due to its flexibility and broad applicability. While existing studies have established regret guarantees under worst-case analysis, they do not capture how performance depends on the variability of the interaction between the learner and the environment. In this paper, we develop a new theoretical analysis for MNL-based Markov decision processes that yields explicit variance-adaptive regret bounds. Our algorithm is computationally efficient and achieves the instance-wise optimal rate of regret, narrowing the gap between upper and lower bounds. Our numerical experiments validate that our method learns optimal policies more efficiently than conventional approaches.

Madhumitha Shridharan, Garud Iyengar

We consider the problem of computing bounds for causal queries on causal graphs with unobserved confounders and discrete valued observed variables, where identifiability does not hold. Existing non-parametric approaches for computing such bounds use linear programming (LP) formulations that quickly become intractable for existing solvers because the size of the LP grows exponentially in the number of edges in the causal graph. We show that this LP can be significantly pruned, allowing us to compute bounds for significantly larger causal inference problems compared to existing techniques. This pruning procedure allows us to compute bounds in closed form for a special class of problems, including a well-studied family of problems where multiple confounded treatments influence an outcome. We extend our pruning methodology to fractional LPs which compute bounds for causal queries which incorporate additional observations about the unit. We show that our methods provide significant runtime improvement compared to benchmarks in experiments and extend our results to the finite data setting. For causal inference without additional observations, we propose an efficient greedy heuristic that produces high quality bounds, and scales to problems that are several orders of magnitude larger than those for which the pruned LP can be solved.

Garud Iyengar, Henry Lam, Tianyu Wang

In data-driven optimization, the sample performance of the obtained decision typically incurs an optimistic bias against the true performance, a phenomenon commonly known as the Optimizer's Curse and intimately related to overfitting in machine learning. Common techniques to correct this bias, such as cross-validation, require repeatedly solving additional optimization problems and are therefore computationally expensive. We develop a general bias correction approach, building on what we call Optimizer's Information Criterion (OIC), that directly approximates the first-order bias and does not require solving any additional optimization problems. Our OIC generalizes the celebrated Akaike Information Criterion to evaluate the objective performance in data-driven optimization, which crucially involves not only model fitting but also its interplay with the downstream optimization. As such it can be used for decision selection instead of only model selection. We apply our approach to a range of data-driven optimization formulations comprising empirical and parametric models, their regularized counterparts, and furthermore contextual optimization. Finally, we provide numerical validation on the superior performance of our approach under synthetic and real-world datasets.

Garud Iyengar, Henry Lam, Tianyu Wang

Empirical risk minimization (ERM) and distributionally robust optimization (DRO) are popular approaches for solving stochastic optimization problems that appear in operations management and machine learning. Existing generalization error bounds for these methods depend on either the complexity of the cost function or dimension of the random perturbations. Consequently, the performance of these methods can be poor for high-dimensional problems with complex objective functions. We propose a simple approach in which the distribution of random perturbations is approximated using a parametric family of distributions. This mitigates both sources of complexity; however, it introduces a model misspecification error. We show that this new source of error can be controlled by suitable DRO formulations. Our proposed parametric DRO approach has significantly improved generalization bounds over existing ERM and DRO methods and parametric ERM for a wide variety of settings. Our method is particularly effective under distribution shifts and works broadly in contextual optimization. We also illustrate the superior performance of our approach on both synthetic and real-data portfolio optimization and regression tasks.

Garud Iyengar, Yu-Shiou Willy Lin, Kaizheng Wang

As generative AI models are increasingly used to simulate real-world systems, quantifying the ``sim-to-real'' gap is critical. The distributional discrepancy between real and simulated outputs is a random variable driven by the stochastic input scenario. A fundamental challenge is that for any given input, the ground-truth and simulated output distributions are only observable through finite batches of samples, often of heterogeneous sizes. This renders standard predictive inference methods inapplicable, as they seek to quantify uncertainty in observable outputs rather than their underlying population parameters. To address this, we construct confidence sets for these latent parameters and use them to derive a robust proxy for the sim-to-real discrepancy. We then estimate the quantile function of this proxy to provide a comprehensive risk profile of the simulator. Our method is model-agnostic and handles general output spaces, such as categorical survey responses and continuous multi-dimensional sensor data. By rigorously accounting for sampling error, the resulting risk profile supports statistical inference for the real output distribution in a new scenario, the calculation of risk measures like Conditional Value-at-Risk (CVaR), and principled comparisons across simulators. We demonstrate the practical utility of this method by evaluating the alignment of four major LLMs with human populations on the WorldValueBench dataset.

Wonyoung Kim, Sungwoo Park, Garud Iyengar et al.

We study the linear bandit problem that accounts for partially observable features. Without proper handling, unobserved features can lead to linear regret in the decision horizon $T$, as their influence on rewards is unknown. To tackle this challenge, we propose a novel theoretical framework and an algorithm with sublinear regret guarantees. The core of our algorithm consists of (i) feature augmentation, by appending basis vectors that are orthogonal to the row space of the observed features; and (ii) the introduction of a doubly robust estimator. Our approach achieves a regret bound of $\tilde{O}(\sqrt{(d + d_h)T})$, where $d$ is the dimension of the observed features and $d_h$ depends on the extent to which the unobserved feature space is contained in the observed one, thereby capturing the intrinsic difficulty of the problem. Notably, our algorithm requires no prior knowledge of the unobserved feature space, which may expand as more features become hidden. Numerical experiments confirm that our algorithm outperforms both non-contextual multi-armed bandits and linear bandit algorithms depending solely on observed features.

Garud Iyengar, Raghav Singal

The flexibility of choosing the ad action as a function of the consumer state is critical for modern-day marketing campaigns. We study the problem of identifying the optimal sequential personalized interventions that maximize the adoption probability for a new product. We model consumer behavior by a conversion funnel that captures the state of each consumer (e.g., interaction history with the firm) and allows the consumer behavior to vary as a function of both her state and firm's sequential interventions. We show our model captures consumer behavior with very high accuracy (out-of-sample AUC of over 0.95) in a real-world email marketing dataset. However, it results in a very large-scale learning problem, where the firm must learn the state-specific effects of various interventions from consumer interactions. We propose a novel attribution-based decision-making algorithm for this problem that we call model-free approximate Bayesian learning. Our algorithm inherits the interpretability and scalability of Thompson sampling for bandits and maintains an approximate belief over the value of each state-specific intervention. The belief is updated as the algorithm interacts with the consumers. Despite being an approximation to the Bayes update, we prove the asymptotic optimality of our algorithm and analyze its convergence rate. We show that our algorithm significantly outperforms traditional approaches on extensive simulations calibrated to a real-world email marketing dataset.

Tomer Gafni, Garud Iyengar, Assaf Zeevi

We consider an online learning problem in environments with multiple change points. In contrast to the single change point problem that is widely studied using classical "high confidence" detection schemes, the multiple change point environment presents new learning-theoretic and algorithmic challenges. Specifically, we show that classical methods may exhibit catastrophic failure (high regret) due to a phenomenon we refer to as endogenous confounding. To overcome this, we propose a new class of learning algorithms dubbed Anytime Tracking CUSUM (ATC). These are horizon-free online algorithms that implement a selective detection principle, balancing the need to ignore "small" (hard-to-detect) shifts, while reacting "quickly" to significant ones. We prove that the performance of a properly tuned ATC algorithm is nearly minimax-optimal; its regret is guaranteed to closely match a novel information-theoretic lower bound on the achievable performance of any learning algorithm in the multiple change point problem. Experiments on synthetic as well as real-world data validate the aforementioned theoretical findings.

Wonyoung Kim, Garud Iyengar, Assaf Zeevi

We consider Pareto front identification (PFI) for linear bandits (PFILin), i.e., the goal is to identify a set of arms with undominated mean reward vectors when the mean reward vector is a linear function of the context. PFILin includes the best arm identification problem and multi-objective active learning as special cases. The sample complexity of our proposed algorithm is optimal up to a logarithmic factor. In addition, the regret incurred by our algorithm during the estimation is within a logarithmic factor of the optimal regret among all algorithms that identify the Pareto front. Our key contribution is a new estimator that in every round updates the estimate for the unknown parameter along multiple context directions -- in contrast to the conventional estimator that only updates the parameter estimate along the chosen context. This allows us to use low-regret arms to collect information about Pareto optimal arms. Our key innovation is to reuse the exploration samples multiple times; in contrast to conventional estimators that use each sample only once. Numerical experiments demonstrate that the proposed algorithm successfully identifies the Pareto front while controlling the regret.

Min-hwan Oh, Garud Iyengar

We consider a sequential assortment selection problem where the user choice is given by a multinomial logit (MNL) choice model whose parameters are unknown. In each period, the learning agent observes a $d$-dimensional contextual information about the user and the $N$ available items, and offers an assortment of size $K$ to the user, and observes the bandit feedback of the item chosen from the assortment. We propose upper confidence bound based algorithms for this MNL contextual bandit. The first algorithm is a simple and practical method which achieves an $\tilde{\mathcal{O}}(d\sqrt{T})$ regret over $T$ rounds. Next, we propose a second algorithm which achieves a $\tilde{\mathcal{O}}(\sqrt{dT})$ regret. This matches the lower bound for the MNL bandit problem, up to logarithmic terms, and improves on the best known result by a $\sqrt{d}$ factor. To establish this sharper regret bound, we present a non-asymptotic confidence bound for the maximum likelihood estimator of the MNL model that may be of independent interest as its own theoretical contribution. We then revisit the simpler, significantly more practical, first algorithm and show that a simple variant of the algorithm achieves the optimal regret for a broad class of important applications.

Min-hwan Oh, Garud Iyengar, Assaf Zeevi

We consider a stochastic contextual bandit problem where the dimension $d$ of the feature vectors is potentially large, however, only a sparse subset of features of cardinality $s_0 \ll d$ affect the reward function. Essentially all existing algorithms for sparse bandits require a priori knowledge of the value of the sparsity index $s_0$. This knowledge is almost never available in practice, and misspecification of this parameter can lead to severe deterioration in the performance of existing methods. The main contribution of this paper is to propose an algorithm that does not require prior knowledge of the sparsity index $s_0$ and establish tight regret bounds on its performance under mild conditions. We also comprehensively evaluate our proposed algorithm numerically and show that it consistently outperforms existing methods, even when the correct sparsity index is revealed to them but is kept hidden from our algorithm.

Min-hwan Oh, Garud Iyengar

One of the most interesting application scenarios in anomaly detection is when sequential data are targeted. For example, in a safety-critical environment, it is crucial to have an automatic detection system to screen the streaming data gathered by monitoring sensors and to report abnormal observations if detected in real-time. Oftentimes, stakes are much higher when these potential anomalies are intentional or goal-oriented. We propose an end-to-end framework for sequential anomaly detection using inverse reinforcement learning (IRL), whose objective is to determine the decision-making agent's underlying function which triggers his/her behavior. The proposed method takes the sequence of actions of a target agent (and possibly other meta information) as input. The agent's normal behavior is then understood by the reward function which is inferred via IRL. We use a neural network to represent a reward function. Using a learned reward function, we evaluate whether a new observation from the target agent follows a normal pattern. In order to construct a reliable anomaly detection method and take into consideration the confidence of the predicted anomaly score, we adopt a Bayesian approach for IRL. The empirical study on publicly available real-world data shows that our proposed method is effective in identifying anomalies.

Min-hwan Oh, Garud Iyengar

We study an exploration method for model-free RL that generalizes the counter-based exploration bonus methods and takes into account long term exploratory value of actions rather than a single step look-ahead. We propose a model-free RL method that modifies Delayed Q-learning and utilizes the long-term exploration bonus with provable efficiency. We show that our proposed method finds a near-optimal policy in polynomial time (PAC-MDP), and also provide experimental evidence that our proposed algorithm is an efficient exploration method.

Hal Cooper, Garud Iyengar, Ching-Yung Lin

The video game industry is larger than both the film and music industries combined. Recommender systems for video games have received relatively scant academic attention, despite the uniqueness of the medium and its data. In this paper, we introduce a graph-based recommender system that makes use of interactivity, arguably the most significant feature of video gaming. We show that the use of implicit data that tracks user-game interactions and levels of attainment (e.g. Sony Playstation Trophies, Microsoft Xbox Achievements) has high predictive value when making recommendations. Furthermore, we argue that the characteristics of the video gaming hobby (low cost, high duration, socially relevant) make clear the necessity of personalized, individual recommendations that can incorporate social networking information. We demonstrate the natural suitability of graph-query based recommendation for this purpose.

Francois Fagan, Garud Iyengar

Arguably the biggest challenge in applying neural networks is tuning the hyperparameters, in particular the learning rate. The sensitivity to the learning rate is due to the reliance on backpropagation to train the network. In this paper we present the first application of Implicit Stochastic Gradient Descent (ISGD) to train neural networks, a method known in convex optimization to be unconditionally stable and robust to the learning rate. Our key contribution is a novel layer-wise approximation of ISGD which makes its updates tractable for neural networks. Experiments show that our method is more robust to high learning rates and generally outperforms standard backpropagation on a variety of tasks.

Maximilian Haas-Heger, Christos Papadimitriou, Mihalis Yannakakis et al.

This paper studies the problem of passive grasp stability under an external disturbance, that is, the ability of a grasp to resist a disturbance through passive responses at the contacts. To obtain physically consistent results, such a model must account for friction phenomena at each contact; the difficulty is that friction forces depend in non-linear fashion on contact behavior (stick or slip). We develop the first polynomial-time algorithm which either solves such complex equilibrium constraints for two-dimensional grasps, or otherwise concludes that no solution exists. To achieve this, we show that the number of possible `slip states' (where each contact is labeled as either sticking or slipping) that must be considered is polynomial (in fact quadratic) in the number of contacts, and not exponential as previously thought. Our algorithm captures passive response behaviors at each contact, while accounting for constraints on friction forces such as the maximum dissipation principle.

Francois Fagan, Garud Iyengar

Recent neural network and language models rely on softmax distributions with an extremely large number of categories. Since calculating the softmax normalizing constant in this context is prohibitively expensive, there is a growing literature of efficiently computable but biased estimates of the softmax. In this paper we propose the first unbiased algorithms for maximizing the softmax likelihood whose work per iteration is independent of the number of classes and datapoints (and no extra work is required at the end of each epoch). We show that our proposed unbiased methods comprehensively outperform the state-of-the-art on seven real world datasets.

Maximilian Haas-Heger, Garud Iyengar, Matei Ciocarlie

In this paper we focus on the following problem in multi-fingered robotic grasping: assuming that an external wrench is being applied to a grasped object, will the contact forces between the hand and the object, as well as the hand joints, respond in such a way as to preserve quasi-static equilibrium? In particular, we assume that there is no change in the joint torques being actively exerted by the motors; any change in contact forces and joint torques is due exclusively to passive effects arising in response to the external disturbance. Such passive effects include for example joints that are driven by highly geared motors (a common occurence in practice) and thus do not back drive in response to external torques. To account for non- linear phenomena encountered in such cases, and which existing methods do not consider, we formulate the problem as a mixed integer program used in the inner loop of an iterative solver. We present evidence showing that this formulation captures important effects for assessing the stability of a grasp employing some of the most commonly used actuation mechanisms.