Every Call is Precious: Global Optimization of Black-Box Functions with Unknown Lipschitz Constants

Optimizing expensive, non-convex, black-box Lipschitz continuous functions presents significant challenges, particularly when the Lipschitz constant of the underlying function is unknown. Such problems often demand numerous function evaluations to approximate the global optimum, which can be prohibitive in terms of time, energy, or resources. In this work, we introduce Every Call is Precious (ECP), a novel global optimization algorithm that minimizes unpromising evaluations by strategically focusing on potentially optimal regions. Unlike previous approaches, ECP eliminates the need to estimate the Lipschitz constant, thereby avoiding additional function evaluations. ECP guarantees no-regret performance for infinite evaluation budgets and achieves minimax-optimal regret bounds within finite budgets. Extensive ablation studies validate the algorithm's robustness, while empirical evaluations show that ECP outperforms 10 benchmark algorithms including Lipschitz, Bayesian, bandits, and evolutionary methods across 30 multi-dimensional non-convex synthetic and real-world optimization problems, which positions ECP as a competitive approach for global optimization.

Decentralized Projection-free Online Upper-Linearizable Optimization with Applications to DR-Submodular Optimization

We introduce a novel framework for decentralized projection-free optimization, extending projection-free methods to a broader class of upper-linearizable functions. Our approach leverages decentralized optimization techniques with the flexibility of upper-linearizable function frameworks, effectively generalizing traditional DR-submodular function optimization. We obtain the regret of $O(T^{1-\theta/2})$ with communication complexity of $O(T^{\theta})$ and number of linear optimization oracle calls of $O(T^{2\theta})$ for decentralized upper-linearizable function optimization, for any $0\le \theta \le 1$. This approach allows for the first results for monotone up-concave optimization with general convex constraints and non-monotone up-concave optimization with general convex constraints. Further, the above results for first order feedback are extended to zeroth order, semi-bandit, and bandit feedback.

Accelerating Quantum Reinforcement Learning with a Quantum Natural Policy Gradient Based Approach

We address the problem of quantum reinforcement learning (QRL) under model-free settings with quantum oracle access to the Markov Decision Process (MDP). This paper introduces a Quantum Natural Policy Gradient (QNPG) algorithm, which replaces the random sampling used in classical Natural Policy Gradient (NPG) estimators with a deterministic gradient estimation approach, enabling seamless integration into quantum systems. While this modification introduces a bounded bias in the estimator, the bias decays exponentially with increasing truncation levels. This paper demonstrates that the proposed QNPG algorithm achieves a sample complexity of $\tilde{\mathcal{O}}(\epsilon^{-1.5})$ for queries to the quantum oracle, significantly improving the classical lower bound of $\tilde{\mathcal{O}}(\epsilon^{-2})$ for queries to the MDP.

Network Diffuser for Placing-Scheduling Service Function Chains with Inverse Demonstration

Network services are increasingly managed by considering chained-up virtual network functions and relevant traffic flows, known as the Service Function Chains (SFCs). To deal with sequential arrivals of SFCs in an online fashion, we must consider two closely-coupled problems - an SFC placement problem that maps SFCs to servers/links in the network and an SFC scheduling problem that determines when each SFC is executed. Solving the whole SFC problem targeting these two optimizations jointly is extremely challenging. In this paper, we propose a novel network diffuser using conditional generative modeling for this SFC placing-scheduling optimization. Recent advances in generative AI and diffusion models have made it possible to generate high-quality images/videos and decision trajectories from language description. We formulate the SFC optimization as a problem of generating a state sequence for planning and perform graph diffusion on the state trajectories to enable extraction of SFC decisions, with SFC optimization constraints and objectives as conditions. To address the lack of demonstration data due to NP-hardness and exponential problem space of the SFC optimization, we also propose a novel and somewhat maverick approach -- Rather than solving instances of this difficult optimization, we start with randomly-generated solutions as input, and then determine appropriate SFC optimization problems that render these solutions feasible. This inverse demonstration enables us to obtain sufficient expert demonstrations, i.e., problem-solution pairs, through further optimization. In our numerical evaluations, the proposed network diffuser outperforms learning and heuristic baselines, by $\sim$20\% improvement in SFC reward and $\sim$50\% reduction in SFC waiting time and blocking rate.

Align-Pro: A Principled Approach to Prompt Optimization for LLM Alignment

The alignment of large language models (LLMs) with human values is critical as these models become increasingly integrated into various societal and decision-making processes. Traditional methods, such as reinforcement learning from human feedback (RLHF), achieve alignment by fine-tuning model parameters, but these approaches are often computationally expensive and impractical when models are frozen or inaccessible for parameter modification. In contrast, prompt optimization is a viable alternative to RLHF for LLM alignment. While the existing literature has shown empirical promise of prompt optimization, its theoretical underpinning remains under-explored. We address this gap by formulating prompt optimization as an optimization problem and try to provide theoretical insights into the optimality of such a framework. To analyze the performance of the prompt optimization, we study theoretical suboptimality bounds and provide insights in terms of how prompt optimization depends upon the given prompter and target model. We also provide empirical validation through experiments on various datasets, demonstrating that prompt optimization can effectively align LLMs, even when parameter fine-tuning is not feasible.

Stochastic $k$-Submodular Bandits with Full Bandit Feedback

In this paper, we present the first sublinear $\alpha$-regret bounds for online $k$-submodular optimization problems with full-bandit feedback, where $\alpha$ is a corresponding offline approximation ratio. Specifically, we propose online algorithms for multiple $k$-submodular stochastic combinatorial multi-armed bandit problems, including (i) monotone functions and individual size constraints, (ii) monotone functions with matroid constraints, (iii) non-monotone functions with matroid constraints, (iv) non-monotone functions without constraints, and (v) monotone functions without constraints. We transform approximation algorithms for offline $k$-submodular maximization problems into online algorithms through the offline-to-online framework proposed by Nie et al. (2023a). A key contribution of our work is analyzing the robustness of the offline algorithms.

On The Global Convergence Of Online RLHF With Neural Parametrization

The importance of Reinforcement Learning from Human Feedback (RLHF) in aligning large language models (LLMs) with human values cannot be overstated. RLHF is a three-stage process that includes supervised fine-tuning (SFT), reward learning, and policy learning. Although there are several offline and online approaches to aligning LLMs, they often suffer from distribution shift issues. These issues arise from the inability to accurately capture the distributional interdependence between the reward learning and policy learning stages. Consequently, this has led to various approximated approaches, but the theoretical insights and motivations remain largely limited to tabular settings, which do not hold in practice. This gap between theoretical insights and practical implementations is critical. It is challenging to address this gap as it requires analyzing the performance of AI alignment algorithms in neural network-parameterized settings. Although bi-level formulations have shown promise in addressing distribution shift issues, they suffer from the hyper-gradient problem, and current approaches lack efficient algorithms to solve this. In this work, we tackle these challenges employing the bi-level formulation laid out in Kwon et al. (2024) along with the assumption \emph{Weak Gradient Domination} to demonstrate convergence in an RLHF setup, obtaining a sample complexity of $\epsilon^{-\frac{7}{2}}$ . Our key contributions are twofold: (i) We propose a bi-level formulation for AI alignment in parameterized settings and introduce a first-order approach to solve this problem. (ii) We analyze the theoretical convergence rates of the proposed algorithm and derive state-of-the-art bounds. To the best of our knowledge, this is the first work to establish convergence rate bounds and global optimality for the RLHF framework in neural network-parameterized settings.

Dynamic Obstacle Avoidance through Uncertainty-Based Adaptive Planning with Diffusion

By framing reinforcement learning as a sequence modeling problem, recent work has enabled the use of generative models, such as diffusion models, for planning. While these models are effective in predicting long-horizon state trajectories in deterministic environments, they face challenges in dynamic settings with moving obstacles. Effective collision avoidance demands continuous monitoring and adaptive decision-making. While replanning at every timestep could ensure safety, it introduces substantial computational overhead due to the repetitive prediction of overlapping state sequences -- a process that is particularly costly with diffusion models, known for their intensive iterative sampling procedure. We propose an adaptive generative planning approach that dynamically adjusts replanning frequency based on the uncertainty of action predictions. Our method minimizes the need for frequent, computationally expensive, and redundant replanning while maintaining robust collision avoidance performance. In experiments, we obtain a 13.5% increase in the mean trajectory length and a 12.7% increase in mean reward over long-horizon planning, indicating a reduction in collision rates and an improved ability to navigate the environment safely.

Last-Iterate Convergence of General Parameterized Policies in Constrained MDPs

We consider the problem of learning a Constrained Markov Decision Process (CMDP) via general parameterization. Our proposed Primal-Dual based Regularized Accelerated Natural Policy Gradient (PDR-ANPG) algorithm uses entropy and quadratic regularizers to reach this goal. For a parameterized policy class with transferred compatibility approximation error, $\epsilon_{\mathrm{bias}}$, PDR-ANPG achieves a last-iterate $\epsilon$ optimality gap and $\epsilon$ constraint violation (up to some additive factor of $\epsilon_{\mathrm{bias}}$) with a sample complexity of $\tilde{\mathcal{O}}(\epsilon^{-2}\min\{\epsilon^{-2},\epsilon_{\mathrm{bias}}^{-\frac{1}{3}}\})$. If the class is incomplete ($\epsilon_{\mathrm{bias}}>0$), then the sample complexity reduces to $\tilde{\mathcal{O}}(\epsilon^{-2})$ for $\epsilon<(\epsilon_{\mathrm{bias}})^{\frac{1}{6}}$. Moreover, for complete policies with $\epsilon_{\mathrm{bias}}=0$, our algorithm achieves a last-iterate $\epsilon$ optimality gap and $\epsilon$ constraint violation with $\tilde{\mathcal{O}}(\epsilon^{-4})$ sample complexity. It is a significant improvement of the state-of-the-art last-iterate guarantees of general parameterized CMDPs.

A Scalable Quantum Non-local Neural Network for Image Classification

Non-local operations play a crucial role in computer vision enabling the capture of long-range dependencies through weighted sums of features across the input, surpassing the constraints of traditional convolution operations that focus solely on local neighborhoods. Non-local operations typically require computing pairwise relationships between all elements in a set, leading to quadratic complexity in terms of time and memory. Due to the high computational and memory demands, scaling non-local neural networks to large-scale problems can be challenging. This article introduces a hybrid quantum-classical scalable non-local neural network, referred to as Quantum Non-Local Neural Network (QNL-Net), to enhance pattern recognition. The proposed QNL-Net relies on inherent quantum parallelism to allow the simultaneous processing of a large number of input features enabling more efficient computations in quantum-enhanced feature space and involving pairwise relationships through quantum entanglement. We benchmark our proposed QNL-Net with other quantum counterparts to binary classification with datasets MNIST and CIFAR-10. The simulation findings showcase our QNL-Net achieves cutting-edge accuracy levels in binary image classification among quantum classifiers while utilizing fewer qubits.