Real-time learning algorithms slash the cost of uncertainty over long periods.

Systems with random, fluctuating movement often need boundaries to push them back on track. This push is called reflection control. The challenge here is keeping the system under control when its underlying drift and volatility are unknown. The researchers created data-driven algorithms to handle this setup. First, they built a learn-then-optimize method. It gathers data during an exploration stage, estimates the needed parameter, inserts that estimate into an optimality equation, and runs the resulting policy. This delivers an O(\sqrt{T}) finite-time expected regret boundregret boundA mathematical measure of how much worse a strategy performs compared to the ideal one over time., meaning its errors grow slowly over time T. Next, they built adaptive-updating and full-history adaptive-updating algorithms. These continuously adjust the estimates and reflection levels, achieving an improved O(\log T) regret bound. Using all past data, the full-history method performs best in numerical simulations.

Why it matters

This helps anyone controlling systems with random noise and physical limits, like stabilizing devices or managing financial risks. By adapting continuously, these systems can achieve more stable and efficient outcomes in unpredictable environments.

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