Stochastic calculus-guided reinforcement learning: A probabilistic framework for optimal decision-making.

Stochastic Calculus-guided Reinforcement learning (SCRL) is a new way to make decisions in situations where things are uncertain. It uses mathematical principles to make better choices and improve decision-making in complex situations. SCRL works better than traditional Stochastic Reinforcement Learning (SRL) methods. In tests, SCRL showed that it can adapt and perform well. It was better than the SRL methods. SCRL had a lower dispersion value of 63.49 compared to SRL's 65.96. This means SCRL had less variation in its results. SCRL also had lower risks than SRL in the short- and long-term. SCRL's short-term risk value was 0.64, and its long-term risk value was 0.78. SRL's short-term risk value was much higher at 18.64, and its long-term risk value was 10.41. Lower risk values are better because they mean less chance of something going wrong. Overall, SCRL is a better way to make decisions when things are uncertain. It uses math to make smarter choices and has less risk than other methods. Also, different metrics, viz training rewards, learning progress, and rolling averages between SRL and SCRL, were assessed, and the study found that SCRL outperforms well compared to SRL. This makes SCRL very useful for real-world situations where decisions must be made carefully.•By leveraging mathematical principles derived from stochastic calculus, SCRL offers a robust framework for making informed choices and enhancing performance in complex scenarios.•In comparison to traditional SRL methods, SCRL demonstrates superior adaptability and efficacy, as evidenced by empirical tests.