Rui Yuan

Rui Yuan, Simon S. Du, Robert M. Gower et al.

We consider infinite-horizon discounted Markov decision processes and study the convergence rates of the natural policy gradient (NPG) and the Q-NPG methods with the log-linear policy class. Using the compatible function approximation framework, both methods with log-linear policies can be written as inexact versions of the policy mirror descent (PMD) method. We show that both methods attain linear convergence rates and $\tilde{\mathcal{O}}(1/ε^2)$ sample complexities using a simple, non-adaptive geometrically increasing step size, without resorting to entropy or other strongly convex regularization. Lastly, as a byproduct, we obtain sublinear convergence rates for both methods with arbitrary constant step size.

Christoph Bergmeir, Frits de Nijs, Evgenii Genov et al.

Predict+Optimize frameworks integrate forecasting and optimization to address real-world challenges such as renewable energy scheduling, where variability and uncertainty are critical factors. This paper benchmarks solutions from the IEEE-CIS Technical Challenge on Predict+Optimize for Renewable Energy Scheduling, focusing on forecasting renewable production and demand and optimizing energy cost. The competition attracted 49 participants in total. The top-ranked method employed stochastic optimization using LightGBM ensembles, and achieved at least a 2% reduction in energy costs compared to deterministic approaches, demonstrating that the most accurate point forecast does not necessarily guarantee the best performance in downstream optimization. The published data and problem setting establish a benchmark for further research into integrated forecasting-optimization methods for energy systems, highlighting the importance of considering forecast uncertainty in optimization models to achieve cost-effective and reliable energy management. The novelty of this work lies in its comprehensive evaluation of Predict+Optimize methodologies applied to a real-world renewable energy scheduling problem, providing insights into the scalability, generalizability, and effectiveness of the proposed solutions. Potential applications extend beyond energy systems to any domain requiring integrated forecasting and optimization, such as supply chain management, transportation planning, and financial portfolio optimization.

Yogesh Pipada Sunil Kumar, Rui Yuan, Nam Trong Dinh et al.

Energy usage optimal scheduling has attracted great attention in the power system community, where various methodologies have been proposed. However, in real-world applications, the optimal scheduling problems require reliable energy forecasting, which is scarcely discussed as a joint solution to the scheduling problem. The 5\textsuperscript{th} IEEE Computational Intelligence Society (IEEE-CIS) competition raised a practical problem of decreasing the electricity bill by scheduling building activities, where forecasting the solar energy generation and building consumption is a necessity. To solve this problem, we propose a technical sequence for tackling the solar PV and demand forecast and optimal scheduling problems, where solar generation prediction methods and an optimal university lectures scheduling algorithm are proposed.

Carlo Alfano, Rui Yuan, Patrick Rebeschini

Modern policy optimization methods in reinforcement learning, such as TRPO and PPO, owe their success to the use of parameterized policies. However, while theoretical guarantees have been established for this class of algorithms, especially in the tabular setting, the use of general parameterization schemes remains mostly unjustified. In this work, we introduce a novel framework for policy optimization based on mirror descent that naturally accommodates general parameterizations. The policy class induced by our scheme recovers known classes, e.g., softmax, and generates new ones depending on the choice of mirror map. Using our framework, we obtain the first result that guarantees linear convergence for a policy-gradient-based method involving general parameterization. To demonstrate the ability of our framework to accommodate general parameterization schemes, we provide its sample complexity when using shallow neural networks, show that it represents an improvement upon the previous best results, and empirically validate the effectiveness of our theoretical claims on classic control tasks.

Yunxiang Li, Rui Yuan, Chen Fan et al.

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.

Rui Yuan, Robert M. Gower, Alessandro Lazaric

We adapt recent tools developed for the analysis of Stochastic Gradient Descent (SGD) in non-convex optimization to obtain convergence and sample complexity guarantees for the vanilla policy gradient (PG). Our only assumptions are that the expected return is smooth w.r.t. the policy parameters, that its $H$-step truncated gradient is close to the exact gradient, and a certain ABC assumption. This assumption requires the second moment of the estimated gradient to be bounded by $A\geq 0$ times the suboptimality gap, $B \geq 0$ times the norm of the full batch gradient and an additive constant $C \geq 0$, or any combination of aforementioned. We show that the ABC assumption is more general than the commonly used assumptions on the policy space to prove convergence to a stationary point. We provide a single convergence theorem that recovers the $\widetilde{\mathcal{O}}(ε^{-4})$ sample complexity of PG to a stationary point. Our results also affords greater flexibility in the choice of hyper parameters such as the step size and the batch size $m$, including the single trajectory case (i.e., $m=1$). When an additional relaxed weak gradient domination assumption is available, we establish a novel global optimum convergence theory of PG with $\widetilde{\mathcal{O}}(ε^{-3})$ sample complexity. We then instantiate our theorems in different settings, where we both recover existing results and obtain improved sample complexity, e.g., $\widetilde{\mathcal{O}}(ε^{-3})$ sample complexity for the convergence to the global optimum for Fisher-non-degenerated parametrized policies.