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State-Dependent Temperature Control for Langevin Diffusions

arXiv 2011.07456 ↗First posted 15 Nov 2020math.OC cs.LGcited by 20

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Abstract (arXiv)

We study the temperature control problem for Langevin diffusions in the context of non-convex optimization. The classical optimal control of such a problem is of the bang-bang type, which is overly sensitive to errors. A remedy is to allow the diffusions to explore other temperature values and hence smooth out the bang-bang control. We accomplish this by a stochastic relaxed control formulation incorporating randomization of the temperature control and regularizing its entropy. We derive a state-dependent, truncated exponential distribution, which can be used to sample temperatures in a Langevin algorithm, in terms of the solution to an HJB partial differential equation. We carry out a numerical experiment on a one-dimensional baseline example, in which the HJB equation can be easily solved, to compare the performance of the algorithm with three other available algorithms in search of a global optimum.

Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 Nov 2020.

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Citing papers per year: 2021: 4; 2022: 4; 2023: 2; 2024: 4; 2025: 4; 2026: 2.

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  12. 2024Reinforcement Learning for Jump-Diffusions, with Financial Applicationscited by 2
8 more
  1. 2026Discretization error from regularized Reinforcement Learning to continuous-time stochastic controlcited by 2
  2. 2022Uniform Generalization Bound on Time and Inverse Temperature for Gradient Descent Algorithm and its Application to Analysis of Simulated Annealingcited by 0
  3. 2023Accelerating Convergence in Global Non-Convex Optimization with Reversible Diffusioncited by 0
  4. 2023Consensus-based adaptive sampling and approximation for high-dimensional energy landscapescited by 0
  5. 2025Research on Optimal Control Problem Based on Reinforcement Learning under Knightian Uncertaintycited by 0
  6. 2025Mean-Field Langevin Diffusions with Density-dependent Temperaturecited by 0
  7. 2025Risk-Sensitive Q-Learning in Continuous Time with Application to Dynamic Portfolio Selectioncited by 0
  8. 2026Fast PAC Global Optimization via Restarted Langevin: Exploration, Exploitation, and Degenerate Coolingcited by 0