Redwan Ahmed Rizvee

Redwan Ahmed Rizvee, Md. Mosaddek Khan

Quadratic Unconstrained Binary Optimization (QUBO) is a generic technique to model various NP-hard combinatorial optimization problems in the form of binary variables. The Hamiltonian function is often used to formulate QUBO problems where it is used as the objective function in the context of optimization. Recently, PI-GNN, a generic scalable framework, has been proposed to address the Combinatorial Optimization (CO) problems over graphs based on a simple Graph Neural Network (GNN) architecture. Their novel contribution was a generic QUBO-formulated Hamiltonian-inspired loss function that was optimized using GNN. In this study, we address a crucial issue related to the aforementioned setup especially observed in denser graphs. The reinforcement learning-based paradigm has also been widely used to address numerous CO problems. Here we also formulate and empirically evaluate the compatibility of the QUBO-formulated Hamiltonian as the generic reward function in the Reinforcement Learning paradigm to directly integrate the actual node projection status during training as the form of rewards. In our experiments, we observed up to 44% improvement in the RL-based setup compared to the PI-GNN algorithm. Our implementation can be found in https://github.com/rizveeredwan/learning-graph-structure.

Redwan Ahmed Rizvee, Raheeb Hassan, Md. Mosaddek Khan

Quadratic Unconstrained Binary Optimization (QUBO) is a generic technique to model various NP-hard Combinatorial Optimization problems (CO) in the form of binary variables. Ising Hamiltonian is used to model the energy function of a system. QUBO to Ising Hamiltonian is regarded as a technique to solve various canonical optimization problems through quantum optimization algorithms. Recently, PI-GNN, a generic framework, has been proposed to address CO problems over graphs based on Graph Neural Network (GNN) architecture. They introduced a generic QUBO-formulated Hamiltonian-inspired loss function that was directly optimized using GNN. PI-GNN is highly scalable but there lies a noticeable decrease in the number of satisfied constraints when compared to problem-specific algorithms and becomes more pronounced with increased graph densities. Here, We identify a behavioral pattern related to it and devise strategies to improve its performance. Another group of literature uses Reinforcement learning (RL) to solve the aforementioned NP-hard problems using problem-specific reward functions. In this work, we also focus on creating a bridge between the RL-based solutions and the QUBO-formulated Hamiltonian. We formulate and empirically evaluate the compatibility of the QUBO-formulated Hamiltonian as the generic reward function in the RL-based paradigm in the form of rewards. Furthermore, we also introduce a novel Monty Carlo Tree Search-based strategy with GNN where we apply a guided search through manual perturbation of node labels during training. We empirically evaluated our methods and observed up to 44% improvement in the number of constraint violations compared to the PI-GNN.

Mohidul Haque Mridul, Mohammad Foysal Khan, Redwan Ahmed Rizvee et al.

In Multi-agent Reinforcement Learning (MARL), accurately perceiving opponents' strategies is essential for both cooperative and adversarial contexts, particularly within dynamic environments. While Proximal Policy Optimization (PPO) and related algorithms such as Actor-Critic with Experience Replay (ACER), Trust Region Policy Optimization (TRPO), and Deep Deterministic Policy Gradient (DDPG) perform well in single-agent, stationary environments, they suffer from high variance in MARL due to non-stationary and hidden policies of opponents, leading to diminished reward performance. Additionally, existing methods in MARL face significant challenges, including the need for inter-agent communication, reliance on explicit reward information, high computational demands, and sampling inefficiencies. These issues render them less effective in continuous environments where opponents may abruptly change their policies without prior notice. Against this background, we present OPS-DeMo (Online Policy Switch-Detection Model), an online algorithm that employs dynamic error decay to detect changes in opponents' policies. OPS-DeMo continuously updates its beliefs using an Assumed Opponent Policy (AOP) Bank and selects corresponding responses from a pre-trained Response Policy Bank. Each response policy is trained against consistently strategizing opponents, reducing training uncertainty and enabling the effective use of algorithms like PPO in multi-agent environments. Comparative assessments show that our approach outperforms PPO-trained models in dynamic scenarios like the Predator-Prey setting, providing greater robustness to sudden policy shifts and enabling more informed decision-making through precise opponent policy insights.