arXiv subjects

Vaneet Aggarwal

Publications and source records attributed to Vaneet Aggarwal.

At least 127 records · Page 7Linked to original sources

arXiv2024

A Unified Approach for Maximizing Continuous DR-submodular Functions

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 two cases, with the proposed framework matching performance of state-of-the-art approaches in the remaining five cases. Notably, our approach for the stochastic function value-based oracle enables the first regret bounds with bandit feedback for stochastic DR-submodular functions.

cs.LG↗

arXiv2023

Combinatorial Stochastic-Greedy Bandit

We propose a novel combinatorial stochastic-greedy bandit (SGB) algorithm for combinatorial multi-armed bandit problems when no extra information other than the joint reward of the selected set of $n$ arms at each time step $t\in [T]$ is observed. SGB adopts an optimized stochastic-explore-then-commit approach and is specifically designed for scenarios with a large set of base arms. Unlike existing methods that explore the entire set of unselected base arms during each selection step, our SGB algorithm samples only an optimized proportion of unselected arms and selects actions from this subset. We prove that our algorithm achieves a $(1-1/e)$-regret bound of $\mathcal{O}(n^{\frac{1}{3}} k^{\frac{2}{3}} T^{\frac{2}{3}} \log(T)^{\frac{2}{3}})$ for monotone stochastic submodular rewards, which outperforms the state-of-the-art in terms of the cardinality constraint $k$. Furthermore, we empirically evaluate the performance of our algorithm in the context of online constrained social influence maximization. Our results demonstrate that our proposed approach consistently outperforms the other algorithms, increasing the performance gap as $k$ grows.

cs.LG↗

arXiv2023

Terrain-based Coverage Manifold Estimation: Machine Learning, Stochastic Geometry, or Simulation?

Given the necessity of connecting the unconnected, covering blind spots has emerged as a critical task in the next-generation wireless communication network. A direct solution involves obtaining a coverage manifold that visually showcases network coverage performance at each position. Our goal is to devise different methods that minimize the absolute error between the estimated coverage manifold and the actual coverage manifold (referred to as accuracy), while simultaneously maximizing the reduction in computational complexity (measured by computational latency). Simulation is a common method for acquiring coverage manifolds. Although accurate, it is computationally expensive, making it challenging to extend to large-scale networks. In this paper, we expedite traditional simulation methods by introducing a statistical model termed line-of-sight probability-based accelerated simulation. Stochastic geometry is suitable for evaluating the performance of large-scale networks, albeit in a coarse-grained manner. Therefore, we propose a second method wherein a model training approach is applied to the stochastic geometry framework to enhance accuracy and reduce complexity. Additionally, we propose a machine learning-based method that ensures both low complexity and high accuracy, albeit with a significant demand for the size and quality of the dataset. Furthermore, we describe the relationships between these three methods, compare their complexity and accuracy as performance verification, and discuss their application scenarios.

cs.NI↗

arXiv2023

Concave Utility Reinforcement Learning with Zero-Constraint Violations

We consider the problem of tabular infinite horizon concave utility reinforcement learning (CURL) with convex constraints. For this, we propose a model-based learning algorithm that also achieves zero constraint violations. Assuming that the concave objective and the convex constraints have a solution interior to the set of feasible occupation measures, we solve a tighter optimization problem to ensure that the constraints are never violated despite the imprecise model knowledge and model stochasticity. We use Bellman error-based analysis for tabular infinite-horizon setups which allows analyzing stochastic policies. Combining the Bellman error-based analysis and tighter optimization equation, for $T$ interactions with the environment, we obtain a high-probability regret guarantee for objective which grows as $\Tilde{O}(1/\sqrt{T})$, excluding other factors. The proposed method can be applied for optimistic algorithms to obtain high-probability regret bounds and also be used for posterior sampling algorithms to obtain a loose Bayesian regret bounds but with significant improvement in computational complexity.

cs.LG↗

arXiv2023

A Framework for Adapting Offline Algorithms to Solve Combinatorial Multi-Armed Bandit Problems with Bandit Feedback

We investigate the problem of stochastic, combinatorial multi-armed bandits where the learner only has access to bandit feedback and the reward function can be non-linear. We provide a general framework for adapting discrete offline approximation algorithms into sublinear $α$-regret methods that only require bandit feedback, achieving $\mathcal{O}\left(T^\frac{2}{3}\log(T)^\frac{1}{3}\right)$ expected cumulative $α$-regret dependence on the horizon $T$. The framework only requires the offline algorithms to be robust to small errors in function evaluation. The adaptation procedure does not even require explicit knowledge of the offline approximation algorithm -- the offline algorithm can be used as a black box subroutine. To demonstrate the utility of the proposed framework, the proposed framework is applied to diverse applications in submodular maximization. The new CMAB algorithms for submodular maximization with knapsack constraints outperform a full-bandit method developed for the adversarial setting in experiments with real-world data.

cs.LG↗

arXiv2023

Improved Analysis of Sparse Linear Regression in Local Differential Privacy Model

In this paper, we revisit the problem of sparse linear regression in the local differential privacy (LDP) model. Existing research in the non-interactive and sequentially local models has focused on obtaining the lower bounds for the case where the underlying parameter is $1$-sparse, and extending such bounds to the more general $k$-sparse case has proven to be challenging. Moreover, it is unclear whether efficient non-interactive LDP (NLDP) algorithms exist. To address these issues, we first consider the problem in the $ε$ non-interactive LDP model and provide a lower bound of $Ω(\frac{\sqrt{dk\log d}}{\sqrt{n}ε})$ on the $\ell_2$-norm estimation error for sub-Gaussian data, where $n$ is the sample size and $d$ is the dimension of the space. We propose an innovative NLDP algorithm, the very first of its kind for the problem. As a remarkable outcome, this algorithm also yields a novel and highly efficient estimator as a valuable by-product. Our algorithm achieves an upper bound of $\tilde{O}({\frac{d\sqrt{k}}{\sqrt{n}ε}})$ for the estimation error when the data is sub-Gaussian, which can be further improved by a factor of $O(\sqrt{d})$ if the server has additional public but unlabeled data. For the sequentially interactive LDP model, we show a similar lower bound of $Ω({\frac{\sqrt{dk}}{\sqrt{n}ε}})$. As for the upper bound, we rectify a previous method and show that it is possible to achieve a bound of $\tilde{O}(\frac{k\sqrt{d}}{\sqrt{n}ε})$. Our findings reveal fundamental differences between the non-private case, central DP model, and local DP model in the sparse linear regression problem.

cs.LG↗

arXiv2023

Improved Communication Efficiency in Federated Natural Policy Gradient via ADMM-based Gradient Updates

Federated reinforcement learning (FedRL) enables agents to collaboratively train a global policy without sharing their individual data. However, high communication overhead remains a critical bottleneck, particularly for natural policy gradient (NPG) methods, which are second-order. To address this issue, we propose the FedNPG-ADMM framework, which leverages the alternating direction method of multipliers (ADMM) to approximate global NPG directions efficiently. We theoretically demonstrate that using ADMM-based gradient updates reduces communication complexity from ${O}({d^{2}})$ to ${O}({d})$ at each iteration, where $d$ is the number of model parameters. Furthermore, we show that achieving an $ε$-error stationary convergence requires ${O}(\frac{1}{(1-γ)^{2}ε})$ iterations for discount factor $γ$, demonstrating that FedNPG-ADMM maintains the same convergence rate as the standard FedNPG. Through evaluation of the proposed algorithms in MuJoCo environments, we demonstrate that FedNPG-ADMM maintains the reward performance of standard FedNPG, and that its convergence rate improves when the number of federated agents increases.

cs.LG↗

arXiv2023

Tensor Ring Optimized Quantum-Enhanced Tensor Neural Networks

Quantum machine learning researchers often rely on incorporating Tensor Networks (TN) into Deep Neural Networks (DNN) and variational optimization. However, the standard optimization techniques used for training the contracted trainable weights of each model layer suffer from the correlations and entanglement structure between the model parameters on classical implementations. To address this issue, a multi-layer design of a Tensor Ring optimized variational Quantum learning classifier (Quan-TR) comprising cascading entangling gates replacing the fully connected (dense) layers of a TN is proposed, and it is referred to as Tensor Ring optimized Quantum-enhanced tensor neural Networks (TR-QNet). TR-QNet parameters are optimized through the stochastic gradient descent algorithm on qubit measurements. The proposed TR-QNet is assessed on three distinct datasets, namely Iris, MNIST, and CIFAR-10, to demonstrate the enhanced precision achieved for binary classification. On quantum simulations, the proposed TR-QNet achieves promising accuracy of $94.5\%$, $86.16\%$, and $83.54\%$ on the Iris, MNIST, and CIFAR-10 datasets, respectively. Benchmark studies have been conducted on state-of-the-art quantum and classical implementations of TN models to show the efficacy of the proposed TR-QNet. Moreover, the scalability of TR-QNet highlights its potential for exhibiting in deep learning applications on a large scale. The PyTorch implementation of TR-QNet is available on Github:https://github.com/konar1987/TR-QNet/

quant-ph↗

arXiv2023

A Unified Algorithm Framework for Unsupervised Discovery of Skills based on Determinantal Point Process

Learning rich skills under the option framework without supervision of external rewards is at the frontier of reinforcement learning research. Existing works mainly fall into two distinctive categories: variational option discovery that maximizes the diversity of the options through a mutual information loss (while ignoring coverage) and Laplacian-based methods that focus on improving the coverage of options by increasing connectivity of the state space (while ignoring diversity). In this paper, we show that diversity and coverage in unsupervised option discovery can indeed be unified under the same mathematical framework. To be specific, we explicitly quantify the diversity and coverage of the learned options through a novel use of Determinantal Point Process (DPP) and optimize these objectives to discover options with both superior diversity and coverage. Our proposed algorithm, ODPP, has undergone extensive evaluation on challenging tasks created with Mujoco and Atari. The results demonstrate that our algorithm outperforms state-of-the-art baselines in both diversity- and coverage-driven categories.

cs.LG↗

arXiv2023

Domain Adaptive Few-Shot Open-Set Learning

Few-shot learning has made impressive strides in addressing the crucial challenges of recognizing unknown samples from novel classes in target query sets and managing visual shifts between domains. However, existing techniques fall short when it comes to identifying target outliers under domain shifts by learning to reject pseudo-outliers from the source domain, resulting in an incomplete solution to both problems. To address these challenges comprehensively, we propose a novel approach called Domain Adaptive Few-Shot Open Set Recognition (DA-FSOS) and introduce a meta-learning-based architecture named DAFOSNET. During training, our model learns a shared and discriminative embedding space while creating a pseudo open-space decision boundary, given a fully-supervised source domain and a label-disjoint few-shot target domain. To enhance data density, we use a pair of conditional adversarial networks with tunable noise variances to augment both domains closed and pseudo-open spaces. Furthermore, we propose a domain-specific batch-normalized class prototypes alignment strategy to align both domains globally while ensuring class-discriminativeness through novel metric objectives. Our training approach ensures that DAFOS-NET can generalize well to new scenarios in the target domain. We present three benchmarks for DA-FSOS based on the Office-Home, mini-ImageNet/CUB, and DomainNet datasets and demonstrate the efficacy of DAFOS-NET through extensive experimentation

cs.CV↗

arXiv2023

Multi-agent Deep Covering Skill Discovery

The use of skills (a.k.a., options) can greatly accelerate exploration in reinforcement learning, especially when only sparse reward signals are available. While option discovery methods have been proposed for individual agents, in multi-agent reinforcement learning settings, discovering collaborative options that can coordinate the behavior of multiple agents and encourage them to visit the under-explored regions of their joint state space has not been considered. In this case, we propose Multi-agent Deep Covering Option Discovery, which constructs the multi-agent options through minimizing the expected cover time of the multiple agents' joint state space. Also, we propose a novel framework to adopt the multi-agent options in the MARL process. In practice, a multi-agent task can usually be divided into some sub-tasks, each of which can be completed by a sub-group of the agents. Therefore, our algorithm framework first leverages an attention mechanism to find collaborative agent sub-groups that would benefit most from coordinated actions. Then, a hierarchical algorithm, namely HA-MSAC, is developed to learn the multi-agent options for each sub-group to complete their sub-tasks first, and then to integrate them through a high-level policy as the solution of the whole task. This hierarchical option construction allows our framework to strike a balance between scalability and effective collaboration among the agents. The evaluation based on multi-agent collaborative tasks shows that the proposed algorithm can effectively capture the agent interactions with the attention mechanism, successfully identify multi-agent options, and significantly outperforms prior works using single-agent options or no options, in terms of both faster exploration and higher task rewards.

cs.LG↗

arXiv2023

Reinforcement Learning with Delayed, Composite, and Partially Anonymous Reward

We investigate an infinite-horizon average reward Markov Decision Process (MDP) with delayed, composite, and partially anonymous reward feedback. The delay and compositeness of rewards mean that rewards generated as a result of taking an action at a given state are fragmented into different components, and they are sequentially realized at delayed time instances. The partial anonymity attribute implies that a learner, for each state, only observes the aggregate of past reward components generated as a result of different actions taken at that state, but realized at the observation instance. We propose an algorithm named $\mathrm{DUCRL2}$ to obtain a near-optimal policy for this setting and show that it achieves a regret bound of $\tilde{\mathcal{O}}\left(DS\sqrt{AT} + d (SA)^3\right)$ where $S$ and $A$ are the sizes of the state and action spaces, respectively, $D$ is the diameter of the MDP, $d$ is a parameter upper bounded by the maximum reward delay, and $T$ denotes the time horizon. This demonstrates the optimality of the bound in the order of $T$, and an additive impact of the delay.

cs.LG↗

arXiv2023

Statistically Efficient Variance Reduction with Double Policy Estimation for Off-Policy Evaluation in Sequence-Modeled Reinforcement Learning

Offline reinforcement learning aims to utilize datasets of previously gathered environment-action interaction records to learn a policy without access to the real environment. Recent work has shown that offline reinforcement learning can be formulated as a sequence modeling problem and solved via supervised learning with approaches such as decision transformer. While these sequence-based methods achieve competitive results over return-to-go methods, especially on tasks that require longer episodes or with scarce rewards, importance sampling is not considered to correct the policy bias when dealing with off-policy data, mainly due to the absence of behavior policy and the use of deterministic evaluation policies. To this end, we propose DPE: an RL algorithm that blends offline sequence modeling and offline reinforcement learning with Double Policy Estimation (DPE) in a unified framework with statistically proven properties on variance reduction. We validate our method in multiple tasks of OpenAI Gym with D4RL benchmarks. Our method brings a performance improvements on selected methods which outperforms SOTA baselines in several tasks, demonstrating the advantages of enabling double policy estimation for sequence-modeled reinforcement learning.

cs.LG↗

arXiv2023

Scalable Multi-agent Covering Option Discovery based on Kronecker Graphs

Covering skill (a.k.a., option) discovery has been developed to improve the exploration of RL in single-agent scenarios with sparse reward signals, through connecting the most distant states in the embedding space provided by the Fiedler vector of the state transition graph. Given that joint state space grows exponentially with the number of agents in multi-agent systems, existing researches still relying on single-agent skill discovery either become prohibitive or fail to directly discover joint skills that improve the connectivity of the joint state space. In this paper, we propose multi-agent skill discovery which enables the ease of decomposition. Our key idea is to approximate the joint state space as a Kronecker graph, based on which we can directly estimate its Fiedler vector using the Laplacian spectrum of individual agents' transition graphs. Further, considering that directly computing the Laplacian spectrum is intractable for tasks with infinite-scale state spaces, we further propose a deep learning extension of our method by estimating eigenfunctions through NN-based representation learning techniques. The evaluation on multi-agent tasks built with simulators like Mujoco, shows that the proposed algorithm can successfully identify multi-agent skills, and significantly outperforms the state-of-the-art. Codes are available at: https://github.itap.purdue.edu/Clan-labs/Scalable_MAOD_via_KP.

cs.LG↗

arXiv2023

Learning Multi-agent Skills for Tabular Reinforcement Learning using Factor Graphs

Covering skill (a.k.a., option) discovery has been developed to improve the exploration of reinforcement learning in single-agent scenarios with sparse reward signals, through connecting the most distant states in the embedding space provided by the Fiedler vector of the state transition graph. However, these option discovery methods cannot be directly extended to multi-agent scenarios, since the joint state space grows exponentially with the number of agents in the system. Thus, existing researches on adopting options in multi-agent scenarios still rely on single-agent option discovery and fail to directly discover the joint options that can improve the connectivity of the joint state space of agents. In this paper, we show that it is indeed possible to directly compute multi-agent options with collaborative exploratory behaviors among the agents, while still enjoying the ease of decomposition. Our key idea is to approximate the joint state space as a Kronecker graph -- the Kronecker product of individual agents' state transition graphs, based on which we can directly estimate the Fiedler vector of the joint state space using the Laplacian spectrum of individual agents' transition graphs. This decomposition enables us to efficiently construct multi-agent joint options by encouraging agents to connect the sub-goal joint states which are corresponding to the minimum or maximum values of the estimated joint Fiedler vector. The evaluation based on multi-agent collaborative tasks shows that the proposed algorithm can successfully identify multi-agent options, and significantly outperforms prior works using single-agent options or no options, in terms of both faster exploration and higher cumulative rewards.

cs.MA↗

arXiv2023

Noisy Tensor Ring approximation for computing gradients of Variational Quantum Eigensolver for Combinatorial Optimization

Variational Quantum algorithms, especially Quantum Approximate Optimization and Variational Quantum Eigensolver (VQE) have established their potential to provide computational advantage in the realm of combinatorial optimization. However, these algorithms suffer from classically intractable gradients limiting the scalability. This work addresses the scalability challenge for VQE by proposing a classical gradient computation method which utilizes the parameter shift rule but computes the expected values from the circuits using a tensor ring approximation. The parametrized gates from the circuit transform the tensor ring by contracting the matrix along the free edges of the tensor ring. While the single qubit gates do not alter the ring structure, the state transformations from the two qubit rotations are evaluated by truncating the singular values thereby preserving the structure of the tensor ring and reducing the computational complexity. This variation of the Matrix product state approximation grows linearly in number of qubits and the number of two qubit gates as opposed to the exponential growth in the classical simulations, allowing for a faster evaluation of the gradients on classical simulators.

quant-ph↗

arXiv2023

Multi-task Hierarchical Adversarial Inverse Reinforcement Learning

Multi-task Imitation Learning (MIL) aims to train a policy capable of performing a distribution of tasks based on multi-task expert demonstrations, which is essential for general-purpose robots. Existing MIL algorithms suffer from low data efficiency and poor performance on complex long-horizontal tasks. We develop Multi-task Hierarchical Adversarial Inverse Reinforcement Learning (MH-AIRL) to learn hierarchically-structured multi-task policies, which is more beneficial for compositional tasks with long horizons and has higher expert data efficiency through identifying and transferring reusable basic skills across tasks. To realize this, MH-AIRL effectively synthesizes context-based multi-task learning, AIRL (an IL approach), and hierarchical policy learning. Further, MH-AIRL can be adopted to demonstrations without the task or skill annotations (i.e., state-action pairs only) which are more accessible in practice. Theoretical justifications are provided for each module of MH-AIRL, and evaluations on challenging multi-task settings demonstrate superior performance and transferability of the multi-task policies learned with MH-AIRL as compared to SOTA MIL baselines.

cs.LG↗

arXiv2023

On the Global Convergence of Natural Actor-Critic with Two-layer Neural Network Parametrization

Actor-critic algorithms have shown remarkable success in solving state-of-the-art decision-making problems. However, despite their empirical effectiveness, their theoretical underpinnings remain relatively unexplored, especially with neural network parametrization. In this paper, we delve into the study of a natural actor-critic algorithm that utilizes neural networks to represent the critic. Our aim is to establish sample complexity guarantees for this algorithm, achieving a deeper understanding of its performance characteristics. To achieve that, we propose a Natural Actor-Critic algorithm with 2-Layer critic parametrization (NAC2L). Our approach involves estimating the $Q$-function in each iteration through a convex optimization problem. We establish that our proposed approach attains a sample complexity of $\tilde{\mathcal{O}}\left(\frac{1}{ε^{4}(1-γ)^{4}}\right)$. In contrast, the existing sample complexity results in the literature only hold for a tabular or linear MDP. Our result, on the other hand, holds for countable state spaces and does not require a linear or low-rank structure on the MDP.

cs.LG↗