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ECCBO: An Inherently Safe Bayesian Optimization with Embedded Constraint Control for Real-Time Optimization

Dinesh Krishnamoorthy

TL;DR

The paper addresses real-time optimization of processes with unknown costs and constraints, where safety-critical constraints must not be violated. It presents ECCBO, a method that converts the constrained RTO into an unconstrained Bayesian optimization by coupling each constraint to a constraint controller that targets a setpoint $z_i$, so the optimization variables become $\mathbf{x}=[z_1,\dots,z_n,u_{n+1},\dots,u_m]^T$. ECCBO claims zero cumulative constraint violation $\mathcal{V}_T=0$ under a perfect-control assumption, while using a Gaussian process surrogate for the cost $F(\mathbf{x},\mathbf{d})$ in a contextual BO framework; it does not require calibrated GP models for the constraints. The approach is demonstrated on a Williams-Otto reactor, showing safe exploration and rapid convergence, highlighting practical viability for process operations with unknown models.

Abstract

This paper introduces a model-free real-time optimization (RTO) framework based on unconstrained Bayesian optimization with embedded constraint control. The main contribution lies in demonstrating how this approach simplifies the black-box optimization problem while ensuring "always-feasible" setpoints, addressing a critical challenge in real-time optimization with unknown cost and constraints. Noting that controlling the constraint does not require detailed process models, the key idea of this paper is to control the constraints to "some" setpoint using simple feedback controllers. Bayesian optimization then computes the optimum setpoint for the constraint controllers. By searching over the setpoints for the constraint controllers, as opposed to searching directly over the RTO degrees of freedom, this paper achieves an inherently safe and practical model-free RTO scheme. In particular, this paper shows that the proposed approach can achieve zero cumulative constraint violation without relying on assumptions about the Gaussian process model used in Bayesian optimization. The effectiveness of the proposed approach is demonstrated on a benchmark Williams-Otto reactor example.

ECCBO: An Inherently Safe Bayesian Optimization with Embedded Constraint Control for Real-Time Optimization

TL;DR

The paper addresses real-time optimization of processes with unknown costs and constraints, where safety-critical constraints must not be violated. It presents ECCBO, a method that converts the constrained RTO into an unconstrained Bayesian optimization by coupling each constraint to a constraint controller that targets a setpoint , so the optimization variables become . ECCBO claims zero cumulative constraint violation under a perfect-control assumption, while using a Gaussian process surrogate for the cost in a contextual BO framework; it does not require calibrated GP models for the constraints. The approach is demonstrated on a Williams-Otto reactor, showing safe exploration and rapid convergence, highlighting practical viability for process operations with unknown models.

Abstract

This paper introduces a model-free real-time optimization (RTO) framework based on unconstrained Bayesian optimization with embedded constraint control. The main contribution lies in demonstrating how this approach simplifies the black-box optimization problem while ensuring "always-feasible" setpoints, addressing a critical challenge in real-time optimization with unknown cost and constraints. Noting that controlling the constraint does not require detailed process models, the key idea of this paper is to control the constraints to "some" setpoint using simple feedback controllers. Bayesian optimization then computes the optimum setpoint for the constraint controllers. By searching over the setpoints for the constraint controllers, as opposed to searching directly over the RTO degrees of freedom, this paper achieves an inherently safe and practical model-free RTO scheme. In particular, this paper shows that the proposed approach can achieve zero cumulative constraint violation without relying on assumptions about the Gaussian process model used in Bayesian optimization. The effectiveness of the proposed approach is demonstrated on a benchmark Williams-Otto reactor example.
Paper Structure (5 sections, 1 theorem, 11 equations, 2 figures)

This paper contains 5 sections, 1 theorem, 11 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Bayesian Optimization with embedded constraint control (ECCBO)
  4. Illustrative example
  5. Conclusion

Key Result

Theorem 1

Under Assumption asm:perfectControl, the ECCBO framework achieves a cumulative violation of $\mathcal{V}_{T} = 0$ for any acquisition function.

Figures (2)

  • Figure 1: Proposed real-time optimization scheme using Bayesian optimization highlighted in gray, with embedded constraint control (ECCBO) highlighted in blue. The process block shown here includes the lower level setpoint control layer and the plant. (a) More degrees of freedom than constraint $m>n$. (b) More constraints than degrees of freedom $m<n$. Note that the process block may further contain lower level regulatory controllers.
  • Figure 2: Simulation results shown the performance of our proposed approach (solid black), compared with the true steady-state optimum (red dashed lines). The decision variable for the Bayesian optimization, namely the setpoint for the constraint controller is shown in yellow solid lines.

Theorems & Definitions (5)

  • Remark 1: Steady-state wait-time
  • Theorem 1
  • proof
  • Remark 2: Regret
  • Remark 3: Overconstrained case $m<n$