This paper integrates machine learning (ML) with mathematical optimization to enhance the efficiency and effectiveness of Unit Commitment (UC) in power systems. UC is a critical operation that determines the optimal commitment status and generation levels of power units to meet system demand while minimizing costs. Traditional mathematical optimization methods, such as Mixed-Integer Linear Programming (MILP), can be time-consuming and struggle with the combinatorial nature of UC, especially with increasing renewable energy integration and intra-hour load variability. The authors propose a synergistic approach that combines Deep Neural Networks (DNNs) with Surrogate Lagrangian Relaxation (SLR), a decomposition and coordination method. SLR reduces the complexity of the original problem by solving subproblems, which are then coordinated to update multipliers. The key contributions include: 1. **Subproblem Learning**: DNNs are used to learn "good enough" solutions for the subproblems, which are significantly easier to solve compared to the original UC problem. The subproblem dimensionality is reduced by aggregating multipliers, and the distribution of random multipliers is specified based on the "jumps" of binary decisions to improve learning efficiency. 2. **Loss Function Design**: An innovative loss function is designed to improve prediction quality, considering both target values and constraint violations. This function includes squared errors and regularization terms to handle binary variables and enforce feasibility. 3. **Graceful Degradation**: For unfamiliar cases where ML predictions are not good enough, Ordinal Optimization (OO) or Branch-and-Cut (B&C) are used as backups to maintain the quality of the overall solution. 4. **Online Self-Learning**: The method integrates online learning to leverage solutions from daily operations, enhancing the DNNs' performance over time. Positive cases (successful predictions) and negative cases (unsuccessful predictions) are used to improve the DNNs' accuracy. The effectiveness of the proposed method is demonstrated through numerical tests on the IEEE 118-bus system and the Polish 2383-bus system. Results show that the method can achieve near-optimal solutions with significantly reduced computational times, making it a promising approach for solving complex UC problems.This paper integrates machine learning (ML) with mathematical optimization to enhance the efficiency and effectiveness of Unit Commitment (UC) in power systems. UC is a critical operation that determines the optimal commitment status and generation levels of power units to meet system demand while minimizing costs. Traditional mathematical optimization methods, such as Mixed-Integer Linear Programming (MILP), can be time-consuming and struggle with the combinatorial nature of UC, especially with increasing renewable energy integration and intra-hour load variability. The authors propose a synergistic approach that combines Deep Neural Networks (DNNs) with Surrogate Lagrangian Relaxation (SLR), a decomposition and coordination method. SLR reduces the complexity of the original problem by solving subproblems, which are then coordinated to update multipliers. The key contributions include: 1. **Subproblem Learning**: DNNs are used to learn "good enough" solutions for the subproblems, which are significantly easier to solve compared to the original UC problem. The subproblem dimensionality is reduced by aggregating multipliers, and the distribution of random multipliers is specified based on the "jumps" of binary decisions to improve learning efficiency. 2. **Loss Function Design**: An innovative loss function is designed to improve prediction quality, considering both target values and constraint violations. This function includes squared errors and regularization terms to handle binary variables and enforce feasibility. 3. **Graceful Degradation**: For unfamiliar cases where ML predictions are not good enough, Ordinal Optimization (OO) or Branch-and-Cut (B&C) are used as backups to maintain the quality of the overall solution. 4. **Online Self-Learning**: The method integrates online learning to leverage solutions from daily operations, enhancing the DNNs' performance over time. Positive cases (successful predictions) and negative cases (unsuccessful predictions) are used to improve the DNNs' accuracy. The effectiveness of the proposed method is demonstrated through numerical tests on the IEEE 118-bus system and the Polish 2383-bus system. Results show that the method can achieve near-optimal solutions with significantly reduced computational times, making it a promising approach for solving complex UC problems.