More Like this

1. A Unified Approach for Maximizing Continuous DR-submodular Functions

   Pedramfar, Mohammad; Quinn, Christopher; Aggarwal, Vaneet (December 2023, Curran Associates, Inc.)

   Oh, A; Naumann, T; Globerson, A; Saenko, K; Hardt, M; Levine, S (Ed.)

   This paper presents a unified approach for maximizing continuous DR-submodular functions that encompasses a range of settings and oracle access types. Our approach includes a Frank-Wolfe type offline algorithm for both monotone and non-monotone functions, with different restrictions on the general convex set. We consider settings where the oracle provides access to either the gradient of the function or only the function value, and where the oracle access is either deterministic or stochastic. We determine the number of required oracle accesses in all cases. Our approach gives new/improved results for nine out of the sixteen considered cases, avoids computationally expensive projections in three cases, with the proposed framework matching performance of state-of-the-art approaches in the remaining four cases. Notably, our approach for the stochastic function value-based oracle enables the first regret bounds with bandit feedback for stochastic DR-submodular functions. 

   more » « less
2. Structured Reinforcement Learning for Incentivized Stochastic Covert Optimization

   https://doi.org/10.1109/LCSYS.2024.3406543  

   Jain, Adit; Krishnamurthy, Vikram (January 2024, IEEE Control Systems Letters)

   This letter studies how a stochastic gradient algorithm (SG) can be controlled to hide the estimate of the local stationary point from an eavesdropper. Such prob- lems are of significant interest in distributed optimization settings like federated learning and inventory management. A learner queries a stochastic oracle and incentivizes the oracle to obtain noisy gradient measurements and per- form SG. The oracle probabilistically returns either a noisy gradient of the function or a non-informative measure- ment, depending on the oracle state and incentive. The learner’s query and incentive are visible to an eavesdropper who wishes to estimate the stationary point. This letter formulates the problem of the learner performing covert optimization by dynamically incentivizing the stochastic oracle and obfuscating the eavesdropper as a finite-horizon Markov decision process (MDP). Using conditions for interval-dominance on the cost and transition probability structure, we show that the optimal policy for the MDP has a monotone threshold structure. We propose searching for the optimal stationary policy with the threshold structure using a stochastic approximation algorithm and a multi– armed bandit approach. The effectiveness of our methods is numerically demonstrated on a covert federated learning hate-speech classification task. 

   more » « less
3. Stochastic Zeroth-Order Functional Constrained Optimization: Oracle Complexity and Applications

   https://doi.org/10.1287/ijoo.2022.0085  

   Nguyen, Anthony; Balasubramanian, Krishnakumar (November 2022, INFORMS Journal on Optimization)

   Functionally constrained stochastic optimization problems, where neither the objective function nor the constraint functions are analytically available, arise frequently in machine learning applications. In this work, assuming we only have access to the noisy evaluations of the objective and constraint functions, we propose and analyze stochastic zeroth-order algorithms for solving this class of stochastic optimization problem. When the domain of the functions is [Formula: see text], assuming there are m constraint functions, we establish oracle complexities of order [Formula: see text] and [Formula: see text] in the convex and nonconvex settings, respectively, where ϵ represents the accuracy of the solutions required in appropriately defined metrics. The established oracle complexities are, to our knowledge, the first such results in the literature for functionally constrained stochastic zeroth-order optimization problems. We demonstrate the applicability of our algorithms by illustrating their superior performance on the problem of hyperparameter tuning for sampling algorithms and neural network training. Funding: K. Balasubramanian was partially supported by a seed grant from the Center for Data Science and Artificial Intelligence Research, University of California–Davis, and the National Science Foundation [Grant DMS-2053918]. 

   more » « less
4. Unified Projection-Free Algorithms for Adversarial DR-Submodular Optimization

   Pedramfar, Mohammad; Nadew, Yididiya Y; Quinn, Christopher J; Aggarwal; Vaneet (May 2024, The Twelfth International Conference on Learning Representations)

   This paper introduces unified projection-free Frank-Wolfe type algorithms for adversarial continuous DR-submodular optimization, spanning scenarios such as full information and (semi-)bandit feedback, monotone and non-monotone functions, different constraints, and types of stochastic queries. For every problem considered in the non-monotone setting, the proposed algorithms are either the first with proven sub-linear $$\alpha$$-regret bounds or have better $$\alpha$$-regret bounds than the state of the art, where $$\alpha$$ is a corresponding approximation bound in the offline setting. In the monotone setting, the proposed approach gives state-of-the-art sub-linear $$\alpha$$-regret bounds among projection-free algorithms in 7 of the 8 considered cases while matching the result of the remaining case. Additionally, this paper addresses semi-bandit and bandit feedback for adversarial DR-submodular optimization, advancing the understanding of this optimization area. 

   more » « less
5. Approximating the noise sensitivity of a monotone Boolean function

   Rubinfeld, R.; Vasilyan, A. (January 2019, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019)

   The noise sensitivity of a Boolean function f: {0,1}^n - > {0,1} is one of its fundamental properties. For noise parameter delta, the noise sensitivity is denoted as NS_{delta}[f]. This quantity is defined as follows: First, pick x = (x_1,...,x_n) uniformly at random from {0,1}^n, then pick z by flipping each x_i independently with probability delta. NS_{delta}[f] is defined to equal Pr [f(x) != f(z)]. Much of the existing literature on noise sensitivity explores the following two directions: (1) Showing that functions with low noise-sensitivity are structured in certain ways. (2) Mathematically showing that certain classes of functions have low noise sensitivity. Combined, these two research directions show that certain classes of functions have low noise sensitivity and therefore have useful structure. The fundamental importance of noise sensitivity, together with this wealth of structural results, motivates the algorithmic question of approximating NS_{delta}[f] given an oracle access to the function f. We show that the standard sampling approach is essentially optimal for general Boolean functions. Therefore, we focus on estimating the noise sensitivity of monotone functions, which form an important subclass of Boolean functions, since many functions of interest are either monotone or can be simply transformed into a monotone function (for example the class of unate functions consists of all the functions that can be made monotone by reorienting some of their coordinates [O'Donnell, 2014]). Specifically, we study the algorithmic problem of approximating NS_{delta}[f] for monotone f, given the promise that NS_{delta}[f] >= 1/n^{C} for constant C, and for delta in the range 1/n <= delta <= 1/2. For such f and delta, we give a randomized algorithm performing O((min(1,sqrt{n} delta log^{1.5} n))/(NS_{delta}[f]) poly (1/epsilon)) queries and approximating NS_{delta}[f] to within a multiplicative factor of (1 +/- epsilon). Given the same constraints on f and delta, we also prove a lower bound of Omega((min(1,sqrt{n} delta))/(NS_{delta}[f] * n^{xi})) on the query complexity of any algorithm that approximates NS_{delta}[f] to within any constant factor, where xi can be any positive constant. Thus, our algorithm's query complexity is close to optimal in terms of its dependence on n. We introduce a novel descending-ascending view of noise sensitivity, and use it as a central tool for the analysis of our algorithm. To prove lower bounds on query complexity, we develop a technique that reduces computational questions about query complexity to combinatorial questions about the existence of "thin" functions with certain properties. The existence of such "thin" functions is proved using the probabilistic method. These techniques also yield new lower bounds on the query complexity of approximating other fundamental properties of Boolean functions: the total influence and the bias. 

   more » « less