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Multi-Objective Human-in-the-Loop Bayesian Optimization of a Lower-Limb Exoskeleton

Neil Janwani, Matthew T. Lerner, Aaron J. Young, Maegan Tucker

arXiv:2609.30695v1cs.ROcs.HC

TL;DR

HILO personalizes assistive-device control, but optimizing one outcome can conflict with other measures. MO-HILBO uses multi-objective Bayesian optimization to infer Pareto-optimal controllers; validation found these controllers dominated anti-Pareto choices and predicted relative rankings along the front.

  • Problem

    HILO personalizes assistive-device controllers, but optimizing metabolic cost alone can conflict with other important outcomes such as comfort.

    Source: §I · p. 1

  • Method

    MO-HILBO combines a probabilistic surrogate with a multi-objective acquisition function to infer Pareto-optimal controllers and select subsequent queries.

    Source: §I · p. 2, C. Pareto Set Discovery · p. 4

  • Results

    Across subjects, inferred Pareto-set controllers empirically dominated anti-Pareto controllers, and the surrogate predicted relative pairwise ordering for nearly all validation Pareto actions on both objectives.

    Source: §V · p. 7

  • Takeaways & Limitations

    MO-HILBO mapped the three-dimensional action space to a one-dimensional manifold of controllers that trade off the objectives, simplifying the search space for real-time human-in-the-loop tuning.

    Source: §V · p. 7

    Standard Bayesian optimization assumes a stationary objective, which may not capture human adaptation, fatigue, or shifting preferences.

    Source: §VI · p. 7

Abstract

from arXiv · show

Human-in-the-loop optimization (HILO) is a common approach for optimizing the control of assistive devices to account for the wearer's unique biomechanics and subjective preferences. However, despite research suggesting that a person may have a different prioritization of objectives depending on time-varying factors such as the environment, their mood, or energy levels, existing HILO approaches only consider a single objective or enforce a fixed weighting on a set of objectives. Neither approach is capable of representing an individual's preferences over objectives. In this work, we propose Multi-Objective Human-in-the-loop Bayesian Optimization (MO-HILBO), which builds on explicit multi-objective Bayesian optimization to efficiently infer a personalized set of Pareto-optimal controllers. We compare our approach with an existing multi-objective HILO method and experimentally demonstrate MO-HILBO on a lower-limb exoskeleton across two objectives: metabolic cost (efficiency) and ordinal human feedback (comfort). We find that MO-HILBO (1) discovers Pareto-optimal controllers, and (2) that the pairwise ordering of points on the Pareto front itself is consistent with validation trials. Lastly, we open-source mohilo, a Python package for running both HILO and MO-HILBO on wearable devices: https://dynamicmobility.github.io/mohilo/.

I. INTRODUCTION

Personalizing wearable controllers must account for individual biomechanics and preferences, yet optimizing one outcome can conflict with others and fixed weights presuppose known trade-offs. The paper introduces MO-HILBO to infer Pareto-optimal controllers, demonstrated on an exoskeleton using metabolic cost and comfort.

I. INTRODUCTION

  • Under limited budgets, NSGA-II-based multi-objective HILO can find sparse Pareto points and must roll out full parameter generations before updating, whereas MOBO approximates dense Pareto sets.Source: §I · p. 2
  • The paper presents the first known MO-HILBO protocol for wearable devices and provides a Python framework for MO-HILBO and single-objective Bayesian HILO.Source: §I · p. 2
  • MO-HILBO shows improved performance in limited-sample, high-noise regimes compared with previous genetic-based multi-objective HILO approaches.Source: §I · p. 2
  • Validation finds Pareto-optimal points and largely consistent per-user ordering along the front for a single objective.Source: §I · p. 2
  • The protocol optimizes three exoskeleton controller parameters across metabolic cost and subjective comfort.Source: Figure 1 · p. 1, §I · p. 2

II. MO-HILBO

MO-HILBO uses a probabilistic model to infer Pareto-optimal controllers and an acquisition function to choose subsequent queries. Its problem setup seeks controllers that trade off across multiple potentially conflicting objectives.

II. MO-HILBO

  • The MO-GP estimates the Pareto-optimal controller set, while a multi-objective acquisition function selects the next controller to query.The selected acquisition explores the trade-off space to identify a Pareto front with large hypervolume quickly.Source: §II · p. 2
  • The acquisition function can be modified for different end goals, while the package makes MO-HILBO available to practitioners conducting multi-objective HILO.Source: §II · p. 2

A. Problem Setup

  • MO-HILBO seeks actions in an n-parameter space that trade off m objectives, returning non-dominated controllers rather than one jointly optimal controller.Initialization transforms objectives into maximization space, although practical metabolic cost is minimized.Source: A. Problem Setup · pp. 2–3

B. Multi-Objective Gaussian Process

MO-HILBO uses independent Gaussian processes to model costly human-feedback objectives, then iteratively selects controllers, collects feedback, and updates the models. Its acquisition strategy varies objective trade-offs to explore the Pareto set.

B. Multi-Objective Gaussian Process

  • Independent Gaussian processes approximate each costly objective, avoiding the need to evaluate every controller directly with human feedback.Each GP provides a continuous posterior over its objective and a variance-based measure of surrogate confidence.Source: B. Multi-Objective Gaussian Process · p. 3
  • The method uses an ARD squared-exponential kernel, with signal variance and lengthscales describing objective scale and correlation between actions.A minimum lengthscale can be set to prevent overfitting by lengthscale collapse.Source: B. Multi-Objective Gaussian Process · p. 3

C. Pareto Set Discovery

  • The procedure initializes actions, then selects a controller, collects user feedback, and updates the surrogate until the fixed query budget is reached.The budget is chosen in practice to collect as much data as possible without fatiguing the user.Source: C. Pareto Set Discovery · p. 3
  • Decoupled repeated measurements allow one objective to be measured while another is evaluated, shortening collection and improving the surrogate under noisy feedback.The method permits different numbers of repeated measurements for objectives at a given iteration.Source: C. Pareto Set Discovery · pp. 3–4
  • Random trade-off weights let qLogNParEGO explore different objective priorities instead of fixing one weighting as in.The acquisition is a log-domain, noise-aware form of ParEGO; it balances exploration and exploitation when choosing the next controller.Source: C. Pareto Set Discovery · p. 4

III. SYNTHETIC EXPERIMENTS

The synthetic study compares MO-HILBO with NSGA-II under conditions resembling a human-subject study. It assesses sample efficiency and Pareto-front approximation using IGD+ in high-noise, small-budget settings.

III. SYNTHETIC EXPERIMENTS

  • The study compares MO-HILBO with NSGA-II to assess sample efficiency and Pareto-front approximation using IGD+.The paper identifies Zhang et al. as the only other HILO approach it knows of that approximates the Pareto set of controllers.Source: §III · p. 4
  • The test domain mimics a human-subject study by using high noise and a small feedback budget.Source: §III · p. 4
  • A lower IGD+ score is the stated indicator of a more accurate Pareto-front approximation.Source: §III · p. 4

A. Comparison Setup

The synthetic comparison tests ideal-point objectives under noise and varies measurement noise, action dimensionality, and objective count. Across these ablations, MO-HILBO achieves lower IGD+ than NSGA-II.

A. Comparison Setup

  • Each ideal-point objective is optimized at a randomly drawn action, with noise added to represent unavoidable measurement noise in human feedback.The GP's prior noise is set within 30% of the true synthetic noise to mimic uncertainty about measurement noise.Source: A. Comparison Setup · p. 4
  • MO-HILBO achieves lower IGD+ than NSGA-II across ablations varying noise, action dimensions, and objective count.Fig. 3 shows the ablation plots; curves are averaged over 50 runs.Source: A. Comparison Setup · p. 4, Figure 3 · p. 5
  • The study performs 50 runs per ablation and caps synthetic trials at 100 to examine sample-budget effects and inform the experimental protocol.Source: A. Comparison Setup · p. 5

B. Baseline

The baseline is NSGA-II, which ranks a population by non-dominated fronts and crowding distance, then uses crossover and mutation to generate offspring. It does not fit a surrogate model.

B. Baseline

  • NSGA-II ranks sampled points first by non-dominated front and then by crowding distance, favoring isolated points within a front.Source: B. Baseline · p. 5
  • It generates offspring from better-ranked points through crossover and mutation, then truncates the pooled parents and offspring while preserving non-dominated solutions.Source: B. Baseline · p. 5
  • Although NSGA-II is computationally efficient, it fits no surrogate, so its approximation depends on a large number of objective evaluations.The experiment uses population size P = 10, matching the baseline approach.Source: B. Baseline · p. 5

C. Results

In synthetic experiments, MOBO reaches better IGD+ scores than NSGA-II with fewer samples across tested noise, action-dimension, and objective-count settings. Its relative advantage is strongest with high noise, small action spaces, and limited sample budgets.

C. Results

  • Across noise levels, MOBO reaches lower IGD+ than NSGA-II within 40 queries and converges by 100, while NSGA-II slows as noise increases.MOBO’s confidence-aware surrogate resamples regions to estimate true performance and distinguish falsely high-performing actions from non-dominated ones.Source: C. Results · p. 5
  • MOBO converges quickly for n ∈ {1, 2, 3}, but higher action dimensions challenge it even though MOBO n = 4 outperforms NSGA-II n = 4.The higher IGD+ score for MOBO n = 4 indicates the challenge at higher action dimensions.Source: C. Results · p. 5
  • MOBO shows promising performance for m ∈ {2, 3, 4, 5}, while NSGA-II plateaus at higher IGD+ as objective count increases; MOBO’s advantage is clearest with high noise, small action spaces, and limited samples.Source: C. Results · p. 5

IV. HUMAN-STUDY EXPERIMENT

The study demonstrates MO-HILBO on a lower-limb exoskeleton, optimizing three control parameters over metabolic cost and subjective comfort. It also introduces and conducts a validation procedure tailored to multi-objective HILO.

IV. HUMAN-STUDY EXPERIMENT

  • The real-world protocol optimizes three exoskeleton control parameters across metabolic cost and ordinal human feedback for comfort.Source: §IV · p. 5
  • The study formulates and carries out a validation procedure specifically tailored to multi-objective HILO protocols.Source: §IV · p. 5
  • Synthetic-study results informed a 24-query protocol for three parameters and two objectives, chosen to remain feasible without subject fatigue.The prior noise was set to 0.5 in standardized units to address high pilot-study noise and a smaller-than-ideal sample budget.Source: §IV · p. 5

A. Hardware

The study uses a sensor-equipped hip/knee exoskeleton whose data pipeline estimates biological joint moments for device control. For subject MB03, MO-HILBO narrows the controller search from the full action space to a simpler Pareto set.

A. Hardware

  • The exoskeleton combines embedded IMUs, pressure-sensing insoles, and foot IMUs; a temporal convolutional network maps sensor data to biological joint moments for control.Source: A. Hardware · p. 5
  • An onboard Linux computer handles sensor acquisition, model inference, and actuator communication, while an offboard laptop and tablet support device interfacing and comfort feedback.The offboard devices connect through WiFi hosted by the onboard microprocessor.Source: A. Hardware · p. 5
  • For MB03, MO-HILBO reduces the search from the full action box to a simpler, single-dimension Pareto set, with hip flexion scale the primary comfort–efficiency decision variable.MB03’s most comfortable gait had the exoskeleton off, while the most efficient controller used nearly maximal hip flexion torque scale.Source: Figure 4 · p. 6

B. Exoskeleton Controller Parametrization

The controller uses delayed biological joint moments scaled separately during positive and negative phases; the experiment applies assistance at the hip and collects metabolic cost and comfort while participants walk. Validation found Pareto dominance over the anti-Pareto set and largely correct pairwise ordering.

B. Exoskeleton Controller Parametrization

  • The controller parameters are temporal delay δ and separate positive- and negative-phase scaling coefficients β1 and β2 for the estimated biological joint moment.The commanded torque uses β1 during positive moments and β2 during negative moments.Source: B. Exoskeleton Controller… · p. 6
  • Assistance is applied at the hip while knee actuators provide zero torque, reducing the parameter space and experiment duration.Source: B. Exoskeleton Controller… · p. 6

C. Experimental Design

  • Three participants completed a 3–4-hour single-session optimization and validation protocol while walking at 1.2 m/s; metabolic cost and 1–5 comfort ratings were collected.Comfort could be reported once per minute, with up to two further chances to change the response because pilot participants sometimes changed their minds during a trial.Source: C. Experimental Design · p. 6
  • Across subjects, the identified Pareto sets Pareto-dominated sign-flipped anti-Pareto sets and correctly predicted 17/18 pairwise orderings of Pareto-optimal points.Hypervolume scales differ because each subject used a different valid reference point.Source: Table I · p. 6

D. Validation Protocol

MO-HILBO was tested on a lower-limb exoskeleton and validated against unseen controllers. Across subjects, inferred Pareto controllers dominated anti-Pareto alternatives, and predicted pairwise rankings were accurate for nearly all validation Pareto actions on both objectives.

D. Validation Protocol

  • Validation sampled three inferred Pareto actions and three anti-Pareto actions, then assessed Pareto dominance and pairwise ranking accuracy for each objective.Users evaluated the six controllers in randomized order during five-minute treadmill walks at 1.2 m/s.Source: D. Validation Protocol · p. 6

V. RESULTS AND DISCUSSION

  • Validation points unseen during training were spaced across the Pareto front, while subjects’ Pareto sets mostly did not overlap in action space.Some overlap occurred between parts of MB03’s and MB01’s sets; none of the subjects’ Pareto-optimal controllers had high delay.Source: Figure 5 · p. 7
  • Subjects differed in their preferred controller regions: MB02 and MB03 favored low torque for comfort, whereas MB01 favored high flexion and extension torque for both comfort and efficiency.The authors note that prior device experience and other user characteristics may influence where Pareto fronts lie.Source: §V · p. 7
  • Across subjects, MO-HILBO’s inferred Pareto controllers empirically dominated anti-Pareto controllers, and predicted pairwise rankings were accurate for nearly all validation Pareto actions on both objectives.The validation actions had not been seen during training.Source: §V · p. 7
  • The learned Pareto set maps a three-dimensional action space to a one-dimensional trade-off manifold, offering a simpler search space for real-time human-in-the-loop tuning.The authors identify real-time tuning as a future research direction.Source: §V · p. 7

VI. CONCLUSION

  • MO-HILBO was demonstrated on a lower-limb exoskeleton across metabolic cost and comfort within a practical trial budget of T = 24, with future work needed to model adaptation, fatigue, or shifting preferences.The paper also presents a validation procedure for Pareto dominance and relative pairwise rankings.Source: §VI · p. 7
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