The complexity of online decision-making under uncertainty stems from the requirement of finding a balance between exploiting known strategies and exploring new possibilities. Naturally, the uncertainty type plays a crucial role in developing decision-making strategies that manage complexity effectively. In this paper, we focus on a specific form of uncertainty known as epistemic ambivalence (EA), which emerges from conflicting pieces of evidence or contradictory experiences. It creates a delicate interplay between uncertainty and confidence, distinguishing it from epistemic uncertainty that typically diminishes with new information. Indeed, ambivalence can persist even after additional knowledge is acquired. To address this phenomenon, we propose a novel framework, called the epistemically ambivalent Markov decision process (EA-MDP), aiming to understand and control EA in decision-making processes. This framework incorporates the concept of a quantum state from the quantum mechanics formalism, and its core is to assess the probability and reward of every possible outcome. We calculate the reward function using quantum measurement techniques and prove the existence of an optimal policy and an optimal value function in the EA-MDP framework. We also propose the EA-epsilon-greedy Q-learning algorithm. To evaluate the impact of EA on decision-making and the expedience of our framework, we study two distinct experimental setups, namely the two-state problem and the lattice problem. Our results show that using our methods, the agent converges to the optimal policy in the presence of EA.

Synthesizable molecular design (also known as synthesizable molecular optimization) is a fundamental problem in drug discovery, and involves designing novel molecular structures to improve their properties according to drug-relevant oracle functions (i.e., objective) while ensuring synthetic feasibility. However, existing methods are mostly based on random search. To address this issue, in this paper, we introduce a novel approach using the reinforcement learning method with quantum-inspired simulated annealing policy neural network to navigate the vast discrete space of chemical structures intelligently. Specifically, we employ a deterministic REINFORCE algorithm using policy neural networks to output transitional probability to guide state transitions and local search using genetic algorithm to refine solutions to a local optimum within each iteration. Our methods are evaluated with the Practical Molecular Optimization (PMO) benchmark framework with a 10K query budget. We further showcase the competitive performance of our method by comparing it against the state-of-the-art genetic algorithms-based method.