The dependency of the actor on the critic in actor-critic (AC) reinforcement learning means that AC can be characterized as a bilevel optimization (BLO) problem, also called a Stackelberg game. This characterization motivates two modifications to vanilla AC algorithms. First, the critic's update should be nested to learn a best response to the actor's policy. Second, the actor should update according to a hypergradient that takes changes in the critic's behavior into account. Computing this hypergradient involves finding an inverse Hessian vector product, a process that can be numerically unstable. We thus propose a new algorithm, Bilevel Policy Optimization with Nyström Hypergradients (BLPO), which uses nesting to account for the nested structure of BLO, and leverages the Nyström method to compute the hypergradient. Theoretically, we prove BLPO converges to (a point that satisfies the necessary conditions for) a local strong Stackelberg equilibrium in polynomial time with high probability, assuming a linear parametrization of the critic's objective. Empirically, we demonstrate that BLPO performs on par with or better than PPO on a variety of discrete and continuous control tasks.

Photonic neural networks (PNNs), which share the inherent benefits of photonic systems, such as high parallelism and low power consumption, could challenge traditional digital neural networks in terms of energy efficiency, latency, and throughput. However, producing scalable photonic artificial intelligence (AI) solutions remains challenging. To make photonic AI models viable, the scalability problem needs to be solved. Large optical AI models implemented on PNNs are only commercially feasible if the advantages of optical computation outweigh the cost of their input-output overhead. In this Perspective, we discuss how field-programmable metasurface technology may become a key hardware ingredient in achieving scalable photonic AI accelerators and how it can compete with current digital electronic technologies. Programmability or reconfigurability is a pivotal component for PNN hardware, enabling in situ training and accommodating non-stationary use cases that require fine-tuning or transfer learning. Co-integration with electronics, 3D stacking, and large-scale manufacturing of metasurfaces would significantly improve PNN scalability and functionalities. Programmable metasurfaces could address some of the current challenges that PNNs face and enable next-generation photonic AI technology.

Fine-grained economic mapping through urban representation learning has emerged as a crucial tool for evidence-based economic decisions. While existing methods primarily rely on supervised or unsupervised approaches, they often overlook semi-supervised learning in data-scarce scenarios and lack unified multi-task frameworks for comprehensive sectoral economic analysis. To address these gaps, we propose SemiGTX, an explainable semi-supervised graph learning framework for sectoral economic mapping. The framework is designed with dedicated fusion encoding modules for various geospatial data modalities, seamlessly integrating them into a cohesive graph structure. It introduces a semi-information loss function that combines spatial self-supervision with locally masked supervised regression, enabling more informative and effective region representations. Through multi-task learning, SemiGTX concurrently maps GDP across primary, secondary, and tertiary sectors within a unified model. Extensive experiments conducted in the Pearl River Delta region of China demonstrate the model's superior performance compared to existing methods, achieving R2 scores of 0.93, 0.96, and 0.94 for the primary, secondary and tertiary sectors, respectively. Cross-regional experiments in Beijing and Chengdu further illustrate its generality. Systematic analysis reveals how different data modalities influence model predictions, enhancing explainability while providing valuable insights for regional development planning. This representation learning framework advances regional economic monitoring through diverse urban data integration, providing a robust foundation for precise economic forecasting.

End-to-end learning has become a widely applicable and studied problem in training predictive ML models to be aware of their impact on downstream decision-making tasks. These end-to-end models often outperform traditional methods that separate training from the optimization and only myopically focus on prediction error. However, the computational complexity of end-to-end frameworks poses a significant challenge, particularly for large-scale problems. While training an ML model using gradient descent, each time we need to compute a gradient we must solve an expensive optimization problem. We present a meta-optimization method that learns efficient algorithms to approximate optimization problems, dramatically reducing computational overhead of solving the decision problem in general, an aspect we leverage in the training within the end-to-end framework. Our approach introduces a neural network architecture that near-optimally solves optimization problems while ensuring feasibility constraints through alternate projections. We prove exponential convergence, approximation guarantees, and generalization bounds for our learning method. This method offers superior computational efficiency, producing high-quality approximations faster and scaling better with problem size compared to existing techniques. Our approach applies to a wide range of optimization problems including deterministic, single-stage as well as two-stage stochastic optimization problems. We illustrate how our proposed method applies to (1) an electricity generation problem using real data from an electricity routing company coordinating the movement of electricity throughout 13 states, (2) a shortest path problem with a computer vision task of predicting edge costs from terrain maps, (3) a two-stage multi-warehouse cross-fulfillment newsvendor problem, as well as a variety of other newsvendor-like problems.

Optimization proxies - machine learning models trained to approximate the solution mapping of parametric optimization problems in a single forward pass - offer dramatic reductions in inference time compared to traditional iterative solvers. This work investigates the integration of solver sensitivities into such end to end proxies via a Sobolev training paradigm and does so in two distinct settings: (i) fully supervised proxies, where exact solver outputs and sensitivities are available, and (ii) self supervised proxies that rely only on the objective and constraint structure of the underlying optimization problem. By augmenting the standard training loss with directional derivative information extracted from the solver, the proxy aligns both its predicted solutions and local derivatives with those of the optimizer. Under Lipschitz continuity assumptions on the true solution mapping, matching first order sensitivities is shown to yield uniform approximation error proportional to the training set covering radius. Empirically, different impacts are observed in each studied setting. On three large Alternating Current Optimal Power Flow benchmarks, supervised Sobolev training cuts mean squared error by up to 56 percent and the median worst case constraint violation by up to 400 percent while keeping the optimality gap below 0.22 percent. For a mean variance portfolio task trained without labeled solutions, self supervised Sobolev training halves the average optimality gap in the medium risk region (standard deviation above 10 percent of budget) and matches the baseline elsewhere. Together, these results highlight Sobolev training whether supervised or self supervised as a path to fast reliable surrogates for safety critical large scale optimization workloads.

Theory of Mind (ToM), the ability to attribute mental states to others, is fundamental for human social intelligence and a critical capability for advanced Artificial Intelligence. Recent advancements in Large Language Models (LLMs) have shown promising performance on ToM benchmarks, raising the question: Do these benchmarks necessitate explicit human-like reasoning processes, or can models succeed through alternative strategies? We investigate this question empirically by applying Reinforcement Learning (RL) and Supervised Fine-Tuning (SFT) to LLMs of varying scales (0.5B to 7B parameters) and evaluating them across multiple ToM datasets. Our results reveal a scale-dependent impact of RL: while RL significantly improves accuracy and fosters high-quality, interpretable, and transferable belief-tracking reasoning in larger models (7B), it leads to "reasoning collapse" in smaller models ($\leq$3B), where high accuracy and generalization ability are achieved via drastically shortened, less meaningful responses. Surprisingly, further SFT achieves competitive and generalizable performance across these benchmarks, often matching or exceeding RL models in accuracy, despite not being explicitly trained to produce structured reasoning traces. These findings highlight a critical discrepancy between benchmark accuracy and the nature of learned reasoning. Our work suggests that current ToM benchmarks may be solvable without requiring the explicit, human-like simulation of mental states they were designed to probe. LLMs, particularly when scale is limited or training signals focus solely on output correctness, may leverage alternative rules effective for benchmark data structures.

We investigate the usage of Large Language Model (LLM) in collecting high-quality data to warm-start Reinforcement Learning (RL) algorithms for learning in some classical Markov Decision Process (MDP) environments. In this work, we focus on using LLM to generate an off-policy dataset that sufficiently covers state-actions visited by optimal policies, then later using an RL algorithm to explore the environment and improve the policy suggested by the LLM. Our algorithm, LORO, can both converge to an optimal policy and have a high sample efficiency thanks to the LLM's good starting policy. On multiple OpenAI Gym environments, such as CartPole and Pendulum, we empirically demonstrate that LORO outperforms baseline algorithms such as pure LLM-based policies, pure RL, and a naive combination of the two, achieving up to $4 \times$ the cumulative rewards of the pure RL baseline.

Deep Neural Networks (DNNs) are increasingly used in control applications due to their powerful function approximation capabilities. However, many existing formulations focus primarily on tracking error convergence, often neglecting the challenge of identifying the system dynamics using the DNN. This paper presents the first result on simultaneous trajectory tracking and online system identification using a DNN-based controller, without requiring persistent excitation. Two new concurrent learning adaptation laws are constructed for the weights of all the layers of the DNN, achieving convergence of the DNN's parameter estimates to a neighborhood of their ideal values, provided the DNN's Jacobian satisfies a finite-time excitation condition. A Lyapunov-based stability analysis is conducted to ensure convergence of the tracking error, weight estimation errors, and observer errors to a neighborhood of the origin. Simulations performed on a range of systems and trajectories, with the same initial and operating conditions, demonstrated 40.5% to 73.6% improvement in function approximation performance compared to the baseline, while maintaining a similar tracking error and control effort. Simulations evaluating function approximation capabilities on data points outside of the trajectory resulted in 58.88% and 74.75% improvement in function approximation compared to the baseline.

We propose a novel reinforcement learning (RL) design to optimize the charging strategy for autonomous mobile robots in large-scale block stacking warehouses. RL design involves a wide array of choices that can mostly only be evaluated through lengthy experimentation. Our study focuses on how different reward and action space configurations, ranging from flexible setups to more guided, domain-informed design configurations, affect the agent performance. Using heuristic charging strategies as a baseline, we demonstrate the superiority of flexible, RL-based approaches in terms of service times. Furthermore, our findings highlight a trade-off: While more open-ended designs are able to discover well-performing strategies on their own, they may require longer convergence times and are less stable, whereas guided configurations lead to a more stable learning process but display a more limited generalization potential. Our contributions are threefold. First, we extend SLAPStack, an open-source, RL-compatible simulation-framework to accommodate charging strategies. Second, we introduce a novel RL design for tackling the charging strategy problem. Finally, we introduce several novel adaptive baseline heuristics and reproducibly evaluate the design using a Proximal Policy Optimization agent and varying different design configurations, with a focus on reward.

Peter Palensky, Simon H. Tindemans Electrical Sustainable Energy Delft University of T echnology Delft, Netherlands { P .Palensky, S.H.Tindemans}@tudelft.nl Abstract --As the number of rooftop photovoltaic (PV) installations increases, aggregators and system operators are required to monitor and analyze these systems, raising the challenge of integration and management of large, spatially distributed time-series data that are both high-dimensional and affected by missing values. In this work, a probabilistic entity embedding-based clustering framework is proposed to address these problems. Applied to a multi-year residential PV dataset, it produces concise, uncertainty-aware cluster profiles that outperform a physics-based baseline in representativeness and robustness, and support reliable missing-value imputation. A systematic hyperparameter study further offers practical guidance for balancing model performance and robustness. I NTRODUCTION Modern energy systems are undergoing a rapid transformation, increasingly driven by decentralized generation sources, especially rooftop photovoltaic (PV) systems installed across residential and commercial properties.