In this manuscript, we consider a particle in a turbulent flow that swims towards its passive partner to maintain proximity. The particle is controlled by a Reinforcement Learning (RL) agent [1], a methodology in Artificial Intelligence (AI) for solving complex decision-making problems. Unlike other AI methods, RL involves an agent learning through interaction with its environment, balancing exploration and exploitation. Exploration involves trying new actions to gain information about the environment (turbulence), while exploitation uses accumulated knowledge to make optimal decisions. This RL decision-making is linked to the Stochastic Optimal Control (SOC) challenge, where the agent maximizes expected reward under environmental uncertainty. In this study, the reward consists of two competing terms: maintaining distance between the agent and its partner, and penalizing the effort required. Among RL strategies, Actor-Critic (AC) methods [2] combine policy-based actors with reward-based critics. The "actor" suggests actions based on current policy, and the "critic" evaluates these actions, providing feedback to update the policy and reduce learning variance.

This paper addresses the challenge of efficiently solving the optimal power flow problem in real-time electricity markets. The proposed solution, named Physics-Informed Market-Aware Active Set learning OPF (PIMA-AS-OPF), leverages physical constraints and market properties to ensure physical and economic feasibility of market-clearing outcomes. Specifically, PIMA-AS-OPF employs the active set learning technique and expands its capabilities to account for curtailment in load or renewable power generation, which is a common challenge in real-world power systems. The core of PIMA-AS-OPF is a fully-connected neural network that takes the net load and the system topology as input. The outputs of this neural network include active constraints such as saturated generators and transmission lines, as well as non-zero load shedding and wind curtailments. These outputs allow for reducing the original market-clearing optimization to a system of linear equations, which can be solved efficiently and yield both the dispatch decisions and the locational marginal prices (LMPs). The dispatch decisions and LMPs are then tested for their feasibility with respect to the requirements for efficient market-clearing results. The accuracy and scalability of the proposed method is tested on a realistic 1814-bus NYISO system with current and future renewable energy penetration levels.