Tuning particle accelerators with safety constraints using Bayesian optimization

Tuning machine parameters of particle accelerators is a repetitive and time-consuming task that is challenging to automate. While many off-the-shelf optimization algorithms are available, in practice their use is limited because most methods do not account for safety-critical constraints in each iteration, such as loss signals or step-size limitations. One notable exception is safe Bayesian optimization, which is a data-driven tuning approach for global optimization with noisy feedback. We propose and evaluate a step-size limited variant of safe Bayesian optimization on two research facilities of the PSI: (a) the SwissFEL and (b) HIPA. We report promising experimental results on both machines, tuning up to 16 parameters subject to 224 constraints.

Figure 1

The a-linebo algorithm alternates between a local search (left; line 2 to 8 in Algorithm 1) and a line search (right; line 9 to 16 in Algorithm 1). On the left the search domain is restricted to a ball centered around the initial point. On the right, the search domain is chosen as a line in the direction of the estimated steepest ascent. The procedure is repeated at the best point found during the line search.

Figure 2

The plots show one-dimensional slices of a synthetic objective (blue, maximized) and constraints (red). The left, middle and right columns correspond to different GP models with length scales 0.1, 0.2 and 0.5, respectively, on the same objective. We produce such plots live during optimization to evaluate model fit and confidence bands relative to the measurements (crosses). The vertical dashed line indicates the best parameter prior to optimizing the one-dimensional subspace, and the vertical solid line indicates the updated best parameter. Green and red intervals on the x axis correspond to predicted safe and unsafe parameters. Note that the safe region is expanded as more data is collected (cf. top to bottom plot). When choosing hyperparameters such as the kernel length scale, system experts can visually inspect the predicted safe set, and make adjustments accordingly. A smaller length scale leads to a more conservative method that expands the safe set in smaller steps. Note that in the right column, the length scale is chosen too large. At the first evaluation the safe set is predicted incorrectly (see upper right plot), which consequently leads to an unsafe query point (orange circle, bottom plot).

Figure 3

Step-by-step evolution of the target function for the different optimization algorithms. We performed optimization at low beam intensity, using five quadrupole strengths on a manually detuned initial point. The left plot shows the target values. The faint lines represent the measurement of the target function at each step. The solid lines depict the measurement of the target function at the best set of parameters predicted by the optimization models (updated only every five steps). The right plot shows the maximum constraint value at each step, where a value above zero corresponds to a constraint violation. Note that neldermead and a-linebo (unsafe) caused interlocks at step 12 and 19 respectively. Note that the exact values of the corresponding constraint violations are unknown, because the machine protection system stops beam operation before the measurement is registered. cma-es and neldermead caused constraint violations that did not trigger interlocks at steps 12 and 2-4 respectively.

Figure 4

(HIPA) Experiment at high beam intensity with 16 tuning parameters. Both cma-es and c-linebo-loc caused interlocks, and the run was stopped after 50 and 110 steps respectively. Note that the exact constraint value of the constraint violation is not known as the machine protection system prevents the measurement. a-linebo-loc successfully tunes the machine at high intensity (repeated twice). This experiment used an earlier configuration of the linebo methods, where we used a single constraint defined as the maximum over the 224 (normalized) loss signals and no safety margin ($\tau =0$). We think that this configuration led to misspecified confidence intervals, and therefore an interlock of c-linebo-loc. In such an event we recommend to use more conservative hyperparameters.

Figure 5

(HIPA) Observed average step sizes (T-bars: maximum) for different algorithms measured in Euclidean norm distance between parameter vectors with normalized input range (left). The right plot shows time used per step, where the solid part of each bar corresponds to machine evaluation time, and the faint part to compute time (on a single core Intel^© Xeon^© Gold 6140 2.3 GHz with 4 GB RAM), i.e., a-linebo-loc: 1.54 s, a-linebo: 1.72 s, c-linebo: 1.51 s, a-linebo (unsafe): 0.01 s, cma-es: 0.0004 s, neldermead: 0.0004 s. The significant increase in computation time for the constraint method is due to the large number of constraints (224). This can be improved by using a joined covariance matrix for all constraints, see the remarks in 2d. a-linebo and c-linebo are not step-size constrained, which leads to larger machine evaluation times. c-linebo-loc has an explicit step-size limit which leads to shorter machine evaluation times. Note that a-linebo (unsafe) and neldermead caused interlocks after few steps (see Fig. 3).

Figure 6

(SwissFEL) Step-by-step evolution of the SwissFEL single pulse intensity (top) and average step size (T-bars: maximum) during optimization of 24 beam position monitor target values. The results demonstrate that the same methods can be used on different accelerators. We emphasize that, similar to the experiments on HIPA, the step-size constraints did not affect optimization performance while resulting in significantly smaller variation in the input space, and therefore a more stable machine. This can be seen in the top plot, where the faint lines depict the objective value observed at the evaluation points during optimization.

Figure 7

The plots show functions sampled from a Gaussian process defined for different kernels. In addition, the top-right plot shows the mean estimate $\widehat{f}$ along with the 95% confidence bands in gray.

Figure 8

Each plot shows the step size (measured in Euclidean norm) for the different methods. Note that without step-size constraints, linebo takes large steps throughout (top middle/right). We also observed that cma-es was slowly increasing step sizes, likely due to invariant subspaces of the objective. Unsafe linebo and neldermead stopped early because of interlocks, therefore interpretation of the data is limited.