POMO: Policy Optimization with Multiple Optima for Reinforcement Learning (2010.16011v3)

Abstract: In neural combinatorial optimization (CO), reinforcement learning (RL) can turn a deep neural net into a fast, powerful heuristic solver of NP-hard problems. This approach has a great potential in practical applications because it allows near-optimal solutions to be found without expert guides armed with substantial domain knowledge. We introduce Policy Optimization with Multiple Optima (POMO), an end-to-end approach for building such a heuristic solver. POMO is applicable to a wide range of CO problems. It is designed to exploit the symmetries in the representation of a CO solution. POMO uses a modified REINFORCE algorithm that forces diverse rollouts towards all optimal solutions. Empirically, the low-variance baseline of POMO makes RL training fast and stable, and it is more resistant to local minima compared to previous approaches. We also introduce a new augmentation-based inference method, which accompanies POMO nicely. We demonstrate the effectiveness of POMO by solving three popular NP-hard problems, namely, traveling salesman (TSP), capacitated vehicle routing (CVRP), and 0-1 knapsack (KP). For all three, our solver based on POMO shows a significant improvement in performance over all recent learned heuristics. In particular, we achieve the optimality gap of 0.14% with TSP100 while reducing inference time by more than an order of magnitude.

Analysis of "POMO: Policy Optimization with Multiple Optima for Reinforcement Learning"

The paper "POMO: Policy Optimization with Multiple Optima for Reinforcement Learning" by Yeong-Dae Kwon et al. presents an innovative approach to enhance the efficacy of reinforcement learning (RL) in solving combinatorial optimization (CO) problems. The authors introduce Policy Optimization with Multiple Optima (POMO), a novel training and inference method designed to exploit the symmetries inherent in the solutions of CO problems. This technique optimizes the sequential decision-making processes that are typical in neural combinatorial optimization, particularly for NP-hard problems such as the Traveling Salesman Problem (TSP), Capacitated Vehicle Routing Problem (CVRP), and 0-1 Knapsack Problem (KP).

Key Contributions

• Multiple Start Optimization: POMO leverages the existence of multiple optimal solutions by generating diverse solution trajectories through parallel exploration from multiple starting points. This approach effectively maximizes the entropy of initial actions and prevents the premature convergence seen in traditional RL models that rely on a fixed starting point. The model's method of sampling $N$ diverse trajectories rather than repeatedly starting from a pre-set node enhances exploration and learning efficiency.
• Shared Baseline: A critical advancement presented is the use of a shared low-variance baseline across multiple trajectories for policy gradient updates. The shared baseline, derived from the collective outcomes of all trajectories, stabilizes learning by counteracting issues related to variance in the sampled policy gradients. This mechanism allows POMO to be more resilient in avoiding local minima, providing a valuable improvement in neural net training for CO tasks.
• Augmentation-Based Inference: The authors also propose an inference technique that uses instance augmentation to boost performance post-training. These augmentations involve basic transformations that preserve the fundamental structure of the solutions, increasing the diversity of inference samples and improving solution quality with a negligible time penalty. This technique significantly narrows the optimality gap in NP-hard CO problems, providing results close to optimal in a fraction of the time compared to traditional solvers.

Empirical Results

The empirical evaluation of POMO across three distinguished NP-hard problems demonstrates substantial improvements. In TSP, the model achieves an optimality gap as low as 0.14% for TSP100, with reduced inference times by more than an order of magnitude compared to state-of-the-art solvers. POMO's robustness and efficiency are further highlighted in CVRP and KP, where it outperforms traditional RL strategies and often approaches optimal solutions without any domain-specific heuristic tailoring.

Implications and Future Directions

The implications of POMO's approach are significant for both theoretical advancements and practical applications of AI in complex problem-solving. The method's ability to autonomously approximate near-optimal solutions by leveraging intrinsic solution symmetries outlines a path toward more generalized and flexible RL applications in CO. Additionally, POMO could potentially influence improvements in RL architectures by setting a precedent for multi-solution exploitation and state-invariant baselines.

Further research might explore integrating POMO with other heuristic improvement methods to tackle even more complex or dynamic CO problems. The development of auxiliary networks to predict optimal starting nodes could address current limitations and enhance POMO's applicability to diverse problem classes. Additionally, a broader exploration of instance augmentation techniques could uncover new avenues for performance improvements.

In conclusion, the POMO methodology establishes a significant step forward in reinforcement learning for combinatorial optimization, offering a scalable and efficient alternative to current heuristic and RL approaches. This work aligns with ongoing trends in AI toward developing robust, domain-agnostic solvers capable of addressing real-world operational challenges.