We analyze the oracle complexity of the stochastic Halpern iteration with variance reduction, where we aim to approximate fixed-points of nonexpansive and contractive operators in a normed finite-dimensional space. We show that if the underlying stochastic oracle is with uniformly bounded variance, our method exhibits an overall oracle complexity of $\tilde{O}(\varepsilon^{-5})$, improving recent rates established for the stochastic Krasnoselskii-Mann iteration. Also, we establish a lower bound of $\Omega(\varepsilon^{-3})$, which applies to a wide range of algorithms, including all averaged iterations even with minibatching. Using a suitable modification of our approach, we derive a $O(\varepsilon^{-2}(1-\gamma)^{-3})$ complexity bound in the case in which the operator is a $\gamma$-contraction. As an application, we propose new synchronous algorithms for average reward and discounted reward Markov decision processes. In particular, for the average reward, our method improves on the best-known sample complexity.

Planning the movement of the sink to maximize the lifetime in wireless sensor networks is an essential problem of great research challenge and practical value. Many existing mobile sink techniques based on mathematical programming or heuristics have demonstrated the feasibility of the task. Nevertheless, the huge computation consumption or the over-reliance on human knowledge can result in relatively low performance. In order to balance the need for high-quality solutions with the goal of minimizing inference time, we propose a new framework combining heterogeneous graph neural network with deep reinforcement learning to automatically construct the movement path of the sink. Modeling the wireless sensor networks as heterogeneous graphs, we utilize the graph neural network to learn representations of sites and sensors by aggregating features of neighbor nodes and extracting hierarchical graph features. Meanwhile, the multi-head attention mechanism is leveraged to allow the sites to attend to information from sensor nodes, which highly improves the expressive capacity of the learning model. Based on the node representations, a greedy policy is learned to append the next best site in the solution incrementally. We design ten types of static and dynamic maps to simulate different wireless sensor networks in the real world, and extensive experiments are conducted to evaluate and analyze our approach. The empirical results show that our approach consistently outperforms the existing methods on all types of maps.

The traveling purchaser problem (TPP) is an important combinatorial optimization problem with broad applications. Due to the coupling between routing and purchasing, existing works on TPPs commonly address route construction and purchase planning simultaneously, which, however, leads to exact methods with high computational cost and heuristics with sophisticated design but limited performance. In sharp contrast, we propose a novel approach based on deep reinforcement learning (DRL), which addresses route construction and purchase planning separately, while evaluating and optimizing the solution from a global perspective. The key components of our approach include a bipartite graph representation for TPPs to capture the market-product relations, and a policy network that extracts information from the bipartite graph and uses it to sequentially construct the route. One significant benefit of our framework is that we can efficiently construct the route using the policy network, and once the route is determined, the associated purchasing plan can be easily derived through linear programming, while, leveraging DRL, we can train the policy network to optimize the global solution objective. Furthermore, by introducing a meta-learning strategy, the policy network can be trained stably on large-sized TPP instances, and generalize well across instances of varying sizes and distributions, even to much larger instances that are never seen during training. Experiments on various synthetic TPP instances and the TPPLIB benchmark demonstrate that our DRL-based approach can significantly outperform well-established TPP heuristics, reducing the optimality gap by 40%-90%, and also showing an advantage in runtime, especially on large-sized instances.

This paper delves into recent advancements in Quantum Reinforcement Learning (QRL), particularly focusing on non-commutative environments, which represent uncharted territory in this field. Our research endeavors to redefine the boundaries of decision-making by introducing formulations and strategies that harness the inherent properties of quantum systems. At the core of our investigation characterization of the agent's state space within a Hilbert space ($\mathcal{H}$). Here, quantum states emerge as complex superpositions of classical state introducing non-commutative quantum actions governed by unitary operators, necessitating a reimagining of state transitions. Complementing this framework is a refined reward function, rooted in quantum mechanics as a Hermitian operator on $\mathcal{H}$. This reward function serves as the foundation for the agent's decision-making process. By leveraging the quantum Bellman equation, we establish a methodology for maximizing expected cumulative reward over an infinite horizon, considering the entangled dynamics of quantum systems. We also connect the Quantum Bellman Equation to the Degree of Non Commutativity of the Environment, evident in Pure Algebra. We design a quantum advantage function. This ingeniously designed function exploits latent quantum parallelism inherent in the system, enhancing the agent's decision-making capabilities and paving the way for exploration of quantum advantage in uncharted territories. Furthermore, we address the significant challenge of quantum exploration directly, recognizing the limitations of traditional strategies in this complex environment.

The use of Potential Based Reward Shaping (PBRS) has shown great promise in the ongoing research effort to tackle sample inefficiency in Reinforcement Learning (RL). However, the choice of the potential function is critical for this technique to be effective. Additionally, RL techniques are usually constrained to use a finite horizon for computational limitations. This introduces a bias when using PBRS, thus adding an additional layer of complexity. In this paper, we leverage abstractions to automatically produce a "good" potential function. We analyse the bias induced by finite horizons in the context of PBRS producing novel insights. Finally, to asses sample efficiency and performance impact, we evaluate our approach on four environments including a goal-oriented navigation task and three Arcade Learning Environments (ALE) games demonstrating that we can reach the same level of performance as CNN-based solutions with a simple fully-connected network.

This paper introduces the problem of learning to place logic blocks in Field-Programmable Gate Arrays (FPGAs) and a learning-based method. In contrast to previous search-based placement algorithms, we instead employ Reinforcement Learning (RL) with the goal of minimizing wirelength. In addition to our preliminary learning results, we also evaluated a novel decomposition to address the nature of large search space when placing many blocks on a chipboard. Empirical experiments evaluate the effectiveness of the learning and decomposition paradigms on FPGA placement tasks.

Policy gradient is a widely utilized and foundational algorithm in the field of reinforcement learning (RL). Renowned for its convergence guarantees and stability compared to other RL algorithms, its practical application is often hindered by sensitivity to hyper-parameters, particularly the step-size. In this paper, we introduce the integration of the Polyak step-size in RL, which automatically adjusts the step-size without prior knowledge. To adapt this method to RL settings, we address several issues, including unknown f* in the Polyak step-size. Additionally, we showcase the performance of the Polyak step-size in RL through experiments, demonstrating faster convergence and the attainment of more stable policies.

The pursuit of robustness has recently been a popular topic in reinforcement learning (RL) research, yet the existing methods generally suffer from efficiency issues that obstruct their real-world implementation. In this paper, we introduce duple perturbation robustness, i.e. perturbation on both the feature and factor vectors for low-rank Markov decision processes (MDPs), via a novel characterization of $(\xi,\eta)$-ambiguity sets. The novel robust MDP formulation is compatible with the function representation view, and therefore, is naturally applicable to practical RL problems with large or even continuous state-action spaces. Meanwhile, it also gives rise to a provably efficient and practical algorithm with theoretical convergence rate guarantee. Examples are designed to justify the new robustness concept, and algorithmic efficiency is supported by both theoretical bounds and numerical simulations.

In this paper, we investigate an offline reinforcement learning (RL) problem where datasets are collected from two domains. In this scenario, having datasets with domain labels facilitates efficient policy training. However, in practice, the task of assigning domain labels can be resource-intensive or infeasible at a large scale, leading to a prevalence of domain-unlabeled data. To formalize this challenge, we introduce a novel offline RL problem setting named Positive-Unlabeled Offline RL (PUORL), which incorporates domain-unlabeled data. To address PUORL, we develop an offline RL algorithm utilizing positive-unlabeled learning to predict the domain labels of domain-unlabeled data, enabling the integration of this data into policy training. Our experiments show the effectiveness of our method in accurately identifying domains and learning policies that outperform baselines in the PUORL setting, highlighting its capability to leverage domain-unlabeled data effectively.

Supply chain networks in enterprises are typically composed of complex topological graphs involving various types of nodes and edges, accommodating numerous products with considerable demand and supply variability. However, as supply chain networks expand in size and complexity, traditional supply chain planning methods (e.g., those found in heuristic rule-based and operations research-based systems) tend to become locally optimal or lack computational scalability, resulting in substantial imbalances between supply and demand across nodes in the network. This paper introduces a novel Generative AI technique, which we call Generative Probabilistic Planning (GPP). GPP generates dynamic supply action plans that are globally optimized across all network nodes over the time horizon for changing objectives like maximizing profits or service levels, factoring in time-varying probabilistic demand, lead time, and production conditions. GPP leverages attention-based graph neural networks (GNN), offline deep reinforcement learning (Offline RL), and policy simulations to train generative policy models and create optimal plans through probabilistic simulations, effectively accounting for various uncertainties. Our experiments using historical data from a global consumer goods company with complex supply chain networks demonstrate that GPP accomplishes objective-adaptable, probabilistically resilient, and dynamic planning for supply chain networks, leading to significant improvements in performance and profitability for enterprises. Our work plays a pivotal role in shaping the trajectory of AI adoption within the supply chain domain.