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Adaptive Safety Filtering for Frozen ACC Policies via Conformal Residual Calibration

Zhiruo Zhou, Rigaudiere Z. Li, Chen Xiwen, Yucheng Chen, Xiaojun Zhu, Houde Liu

arXiv:2609.35415v1cs.ROcs.CVcs.SYeess.SY

TL;DR

Frozen ACC policies may violate constraints when deployment dynamics differ from training, motivating a runtime filter that adapts to observed mismatch without retraining the policy. RACF calibrates residuals into an operating margin and projects actions through finite dynamics constraints. It achieves higher episode safety than the evaluated nominal CBF-QP baseline, while the matched-hardware comparison finds lower mean amortized rollout time for Adaptive than Robust CBF-QP, which has higher episode safety.

  • Problem

    Deployment shifts in vehicle parameters and lead-vehicle motion can make nominal predictions inaccurate, leaving frozen ACC policies in need of a runtime safety interface.

    Source: §1 · p. 1

  • Method

    RACF calibrates residuals of a fixed nominal predictor into an operating margin and projects frozen-policy actions through finite dynamics constraints, with completed transitions updating margins and candidate selection.

    Source: §1 · p. 1, §3.1 · p. 2

  • Results

    Adaptive RACF has higher episode safety than the evaluated nominal CBF-QP baseline, while in the matched-hardware cohort it has lower mean amortized rollout time and Robust CBF-QP has higher episode safety.

    Source: §6 · p. 4, §3.3 · p. 15

  • Takeaways & Limitations

    The evidence does not establish a universal advantage for online adaptation, since selected fixed margins remain competitive.

    Source: §6 · p. 4

    Adaptive and Envelope relax formal alignment, scaling, feasibility, or fallback premises, so their safety remains empirical.

    Source: §3.3 · p. 15

Abstract

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Frozen adaptive cruise control (ACC) policies can violate constraints when deployment dynamics differ from their training conditions. We propose residual-aware conformal action filtering (RACF), which calibrates residuals of a fixed nominal predictor and converts their quantile into an operating margin for finite-model action projection. Completed transitions update margins and candidate selection without retraining the policy. In a registered comparison over 2,400 controller-trial units, Adaptive RACF achieves 94.3% episode safety, improving by 19.9 percentage points over the evaluated nominal CBF-QP baseline while reducing projection frequency from 8.11% to 6.63%. A controlled study isolates a 4.54-point improvement from residual-margin injection. In a separate matched-hardware evaluation, Adaptive reduces mean amortized rollout time by 21.2% relative to Robust CBF-QP, with 161/180 versus 170/180 safe episodes. We characterize conditions linking one-step residual coverage to constraint satisfaction and quantify the observed safety-computation trade-offs.

1. INTRODUCTION

Deployment shifts in ACC can affect both ego-vehicle dynamics and the lead trajectory, so frozen controllers need runtime safety filtering that limits policy distortion. RACF calibrates predictor residuals into a margin and uses completed transitions to update filtering without retraining the policy.

1. INTRODUCTION

  • Mass, road grade, and actuator gain shift ego dynamics, while braking and stop–go motion change the lead trajectory, creating difficult combined deployment conditions.The introduction identifies absorbing both kinds of mismatch while limiting policy distortion as the filter’s challenge.Source: §1 · p. 1
  • Offline RL methods such as IQL and CQL [3], and cross-domain policy-learning methods, do not remove the need for a runtime safety interface around a frozen controller.Source: §1 · p. 1
  • RACF calibrates residuals of a fixed nominal predictor into an operating margin, then uses finite dynamics constraints and completed transitions to update filtering without changing policy parameters.The paper also characterizes sufficient conditions connecting marginal one-step residual coverage to constraint satisfaction by the applied action.Source: §1 · p. 1
  • The evaluation combines paired ACC comparisons, controlled component studies, and matched-hardware measurements to examine constraint satisfaction, action modification, and computation.Source: §1 · p. 1

2. PROBLEM FORMULATION

The problem is to apply a bounded action close to a frozen policy’s proposal while preserving the filter margin at the next state. The ACC formulation uses fixed normalized coordinates, finite dynamics predictors, and headway and speed margins.

2. PROBLEM FORMULATION

  • The filter seeks the closest bounded applied action to the frozen policy proposal while requiring the next state’s filter margin to remain nonnegative.Policy training precedes calibration and evaluation; filtering does not update policy weights.Source: §2 · p. 1
  • The ACC state comprises ego speed, lead speed, gap, desired speed, and road grade, represented in fixed dimensionless coordinates.The reference units are 1 m/s for speed, 1 m for gap, and 1° for grade.Source: §2 · p. 1
  • The nominal score predictor assumes 1500 kg mass, observed grade, 0.7 actuator gain, constant lead speed, and different drag and rolling coefficients than the simulator.Constraint predictors vary mass, grade, and actuator gain over a finite set; the normalized action maps to the evaluated actuator-force range.Source: §2 · pp. 1–2
  • The filter margin combines dimensionless headway and speed components, with headway based on the standard spacing policy dCTH = d0 + Thve.The paper uses d0 = 3 m, Th = 1.5 s, and vmax = 30 m/s.Source: §2 · p. 2
  • Changing reference units or coordinate weights requires recalibrating the score, margin, and Lipschitz conversion.Source: §2 · p. 2
  • An episode is safe only if every executed transition has nonnegative headway margin and no collision; speed margin remains a filter constraint, while tracking, violation duration, and comfort are separate outcomes.Source: §2 · p. 2

3. RACF METHOD

RACF separates residual calibration from policy optimization: a calibrated mismatch quantile sets an operating margin, and finite-model projection minimally modifies the frozen proposal. Its adaptive variant updates margins and candidate selection from completed transitions, while its formal guarantees rely on stated premises.

3.1. Residual calibration and action projection

  • Projection seeks the smallest feasible change to the frozen policy action while enforcing the margin across active predictors in a finite dynamics bank.Static RACF uses the full candidate set and margin ηqα; the base robust projection sets the margin to zero to isolate the residual-margin effect.Source: §3.1 · p. 2
  • With 500 nominal calibration transitions and α = 0.1, the residual score’s calibrated quantile is qα = 0.09188 and initializes the operating margin.The score captures aggregate one-step predictor mismatch, including unmodeled lead motion.Source: §3.1 · p. 2
  • The score-defining nominal predictor and constraint predictors are separate implementations, and an infeasible solve or failed post-check invokes bounded maximum braking that need not preserve the alignment premise.Source: §3.1 · p. 3

3.2. Adaptive update and operating envelope

  • Adaptive RACF updates candidate-specific quantiles from a 40-transition window and the margin from a separate 100-transition window, using completed transitions to affect the next action.Candidate pruning starts after a 20-transition warm-up and retains at most four candidates near the minimum residual; these empirical rules do not inherit adaptive conformal validity.Source: §3.2 · p. 3
  • Envelope RACF uses a fixed margin B = 0.45, distinct from a calibrated qH; the CBF-QP comparisons instead impose discrete-time barrier constraints on one nominal or all eight hypotheses.The nominal and robust versions share action bounds and bounded-braking fallback.Source: §3.2 · p. 3

4. COVERAGE AND CONDITIONAL SAFETY

The section bounds marginal one-step residual coverage under a distribution-shift premise and states additional conditions for translating that coverage into constraint satisfaction. It distinguishes those conditional results from episode-level guarantees and empirical rollout evidence.

4.1. One-step residual coverage

  • Under dTV(P, QD) ≤ ϵ almost surely, Theorem 1 gives marginal next-score coverage of at least 1 − α − ϵ.The guarantee is over calibration data D and the next deployed score S0,*; it is neither state/history-conditional nor simultaneous across steps.Source: §4.1 · p. 3

4.2. Residual-to-safety conversion

  • The same 1 − α − ϵ one-step lower bound transfers to constraint satisfaction only if the final applied action, including fallback, satisfies the aligned Lipschitz-scaled nominal constraint.On the stated ACC state domain, filter-barrier satisfaction implies headway of at least 3 m, above the 0.5 m collision threshold; outside it, only barrier satisfaction follows.Source: §4.2 · p. 3

4.3. Practical realizability and premises

  • Episode-max calibration requires a deployment shift bound, and changing the filter using its calibrated quantile changes the law, requiring fresh calibration or another bound.The authors distinguish these premises from empirical online updates and state that rollout and trace analyses do not establish a closed-loop certificate.Source: §4.3 · p. 3

5. EXPERIMENTS

Experiments compare frozen ACC policies and filters in paired partial rollouts, then test residual-margin and candidate-selection components and matched-hardware computation. Adaptive RACF improves safety over the nominal CBF-QP baseline, while its hardware comparison with Robust CBF-QP shows a safety–runtime trade-off.

5.1. Evaluation setup

  • The registered evaluation pairs policies across four physical conditions, two lead scenarios, and 25 shared resets per cell (2,400 units; H = 500), excluding state-estimation error.Paired comparisons share policy, condition, scenario, trial, seed, initial state, and lead trajectory.Source: §5.1 · p. 3

5.2. Registered comparison

  • 94.3% episode safety (2262/2400) for Adaptive versus 74.4% (1785/2400) for nominal CBF-QP, a 19.9-pp gain, with projection frequency falling from 8.11% to 6.63%.Table 1 compares complete configurations.Source: §5.2 · p. 3
  • Adaptive exceeded ACI and CPSF-style safety by 5.21 pp [3.96, 6.54] and 5.50 pp [4.25, 6.83], respectively; both are frozen one-step interfaces.All five methods had zero observed collisions.Source: §5.2 · p. 4

5.3. Controlled component studies

  • 4.54 pp [3.63, 5.54] higher safety followed residual-margin injection when candidates, objective, solver, bounds, and fallback were fixed.The comparison rose from 1993/2400 to 2102/2400 safe episodes.Source: §5.3 · p. 4
  • In the separate 180-unit ablation, margin-only and joint configurations reached 161/180 safe episodes versus 144/180 for candidate-only and Static; candidate selection had no independent binary safety gain.The matched candidate-set × margin ablation is shown in Fig. 2(b).Source: §5.3 · p. 4, Figure 2 · p. 4
  • On another development/test split, Adaptive was 2.22 pp below selected fixed margins [−5.56, 0.56], showing neither superiority nor equivalence.An offline floor raised rolling/ACI coverage without changing paired safety.Source: §5.3 · p. 4

5.4. Computational cost and diagnostics

  • Adaptive’s mean amortized rollout time was 21.2% lower than Robust CBF-QP, while Robust CBF-QP had 170/180 versus Adaptive’s 161/180 safe episodes.This balanced-order matched-hardware comparison covers complete implementations and does not isolate candidate selection.Source: §5.4 · p. 4, §5.2 · p. 4

6. DISCUSSION AND CONCLUSION

RACF filters actions for frozen ACC policies using residual-driven margins and finite model hypotheses. The evidence supports higher safety than the evaluated nominal CBF-QP baseline and a controlled residual-margin benefit, but does not establish a universal advantage for online adaptation.

6. Discussion and conclusion

  • RACF provides residual-driven action filtering for frozen ACC policies; controlled tests identify a residual-margin benefit, while selected fixed margins remain competitive.The discussion reports that Adaptive has lower mean amortized rollout time, while Robust CBF-QP has higher episode safety in that cohort.Source: §6 · p. 4
  • Evidence is limited to simulated ACC, an eight-model library, and simulator-state access; larger libraries, estimated states, and target-hardware evaluation remain future work.The paper also states that its conditional coverage-to-safety analysis depends on explicit premises.Source: §6 · p. 4

1. SUPPLEMENTARY EXPERIMENTS

These supplementary ACC partial-rollout studies test residual-margin and adaptive filtering across safety, control-cost, horizon, and predictor-alignment settings. They also examine when one-step residual coverage does not extend to episode-level safety.

1.1. Evaluation protocol

  • The evaluation uses paired ACC partial rollouts with shared policy, condition, scenario, trial, seed, initial state, and lead trajectory.The main comparison includes 12 frozen controllers, four physical conditions, two lead scenarios, 25 resets per cell, and H = 500.Source: §1.1 · p. 6

1.2. Controlled RACF decomposition

  • Adding the calibrated margin raises episode-safe rollouts from 1,993/2,400 to 2,102/2,400, a paired gain of 4.54 points (95% CI [3.63,5.54]).With projection and other settings fixed, jerk P95 rises by 0.240 m/s3; in a separate matched cohort, Adaptive reaches 622/720 safe rollouts versus 595/720 for Static, a 3.75-point gain.Source: §1.2 · p. 6

1.3. Absolute filters and candidate set

  • Robust CBF-QP enforces all eight candidate barrier constraints and had the highest episode-safe rate among evaluated methods in the registered cohort.The controlled decomposition isolates adding the calibrated residual margin to otherwise identical robust projection; it does not compare calibration with alternative margin-selection procedures.Source: §1.3 · p. 6

1.4. Safety-first control-cost selection

  • B = 0.45 reached 320/360 safe rollouts (+11.94 points [8.61,15.28]); the matched Adaptive–Static comparison was 318/360 versus 302/360 (+4.44 points).None of the three smoothing weights met all four safety, collision, jerk, and tracking requirements, so subsequent experiments retained the original envelope and predicted-safety priority.Source: §1.4 · p. 7

1.5. Coverage, horizon, and deployment results

  • 184 configuration-level observations had at least 90% independent one-step coverage but an episode-level violation; 97.48% of exceedances fell in lead-acceleration intervals.Retrospectively adding lead modes {−4, 0, 2} reduced the maximum to 0.0035 and covered 120/120 inspected episodes.Source: §1.5 · p. 7
  • Across horizons H = 100 to 500, Adaptive/Envelope safety changed from 100 to 87.5%, while Robust CBF-QP remained at 98.3%.A 20-step OSQP MPC solved all 100,000 programs but obtained 0/200 headway-safe trajectories, making it a model-mismatch comparison outside the ranking.Source: §1.5 · p. 7

1.6. Implementation details

  • Adaptive RACF updates candidate-specific quantiles every ten completed transitions after a 20-transition warm-up, while a separate 100-transition window updates the operating margin.The implementation uses SLSQP with at most 40 iterations and bounded maximum braking after infeasible or unsuccessful solves.Source: §1.6 · p. 9

1.7. Predictor-alignment study

  • In the predictor-alignment cohort, the aligned variant reached 149/180 safe episodes, versus 144/180 for Static and 170/180 for Robust CBF-QP.The margin-fit condition qH ≤ qα was not met, so these results are operating-point evidence rather than a pathwise guarantee; candidate-only matched Static, while margin-only and joint updates each reached 161/180.Source: §1.7 · p. 10

2. ADDITIONAL EXPERIMENTS AND ANALYSES

The section standardizes safety and intervention measures, tests candidate and margin updates in a shared-unit ablation, and reports matched adaptive–static comparisons on independent test seeds.

2.1. Unified endpoint and fallback definitions

  • The primary episode-safe endpoint requires nonnegative headway margin at every executed transition and no collision; projection, action correction, jerk, and fallback are separately defined.The dual endpoint additionally requires the speed margin and remains a labelled diagnostic.Source: §2.1 · p. 10

2.2. Candidate–margin 2×2 ablation

  • The ablation’s observed binary safety gain is attributable to margin adaptation; candidate updates show no separate observed binary gain.Action-correction differences were +0.00019, +0.00075, −0.00008, and +0.00047, while jerk-P95 differences were +0.0616, +0.0206, +0.0415, and +0.0004 in the same order.Source: §2.2 · p. 10

2.3. Intervention-matched Pareto comparison

  • Figure 3 compares safety across predictor-alignment conditions, component updates, and episode-max residual quantile with stopped-episode coverage.The transfer series changes the controller and is descriptive.Source: Figure 3 · p. 11
  • The matched comparison retained 40 of 48 adaptive–static choices, producing 400 paired test units; eight unmatched choices were excluded.Matching required projection-rate error at most 0.005 and relative action-correction error at most 0.10; the partial rollout does not establish a global Pareto frontier.Source: §2.3 · p. 11

2.4. Predictor alignment and fallback analysis

The predictor-alignment analysis reports safety and fallback outcomes without observing a strict implication failure, while the isolated adaptive conformal baseline has lower episode safety than adaptive RACF and imperfect rolling coverage.

2.4. Predictor alignment and fallback analysis

  • 149/180 evaluation episodes were safe for predictor-aligned RACF, with fallback on 1,224/90,000 steps and no observed strict implication failure.The analysis keeps the nominal predictor f0 present at all steps and uses m = Lhqα = 0.1656329484.Source: §2.4 · p. 11
  • Emergency fallback can leave a negative robust constraint, so the observed safety results have limited interpretation and do not establish a guarantee.The transfer variant is an empirical diagnostic, not a guarantee.Source: §2.4 · p. 11

2.5. Rolling coverage and adaptive conformal baseline

  • Adaptive RACF was safe in 161/180 episodes versus 143/180 for isolated ACI; rolling coverage was 0.8997 before step 100 and 0.8675 after step 100.The 50-step rolling window and episode miscoverage mean of 0.1261 do not establish adaptive conformal validity or a closed-loop safety guarantee.Source: §2.5 · pp. 11–12
  • Figure 5 plots ACI and fixed-q0 coverage over a 50-step rolling window, with step 100 and the 0.90 target marked.The curves coincide where coverage values agree.Source: Figure 5 · p. 12

2.6. External CPSF-style comparator

The external finite predictive-set comparator matches static RACF but trails adaptive RACF in the reported cohort; additional analyses describe residual-event alignments, development-only shift evidence, and host-specific CPU timing.

2.6. External CPSF-style comparator

  • The one-step finite predictive-set comparator achieved 144/180 safety, equal to static RACF and 9.44 percentage points below adaptive RACF.It is not a multi-step backup or viability predictive safety filter reproduction; the comparison is empirical only.Source: §2.6 · p. 12

2.7. Dynamic recovery and out-of-grid evidence

  • Margin response occurred for 360/360 observable strong-residual proxy events, candidate broadening for 249/360, first action intervention for 155/360, and ten-step residual recovery for 360/360.These are proxy alignments, not causal selector-trigger labels; the mass and four-axis extensions are development partial-rollout evidence, not generalization or full-benchmark claims.Source: §2.7 · p. 12

2.8. Runtime and utility boundary

  • The real CPU probe measured a 1.992 ms episode-mean warm per-step policy–filter stage and a 2.781 ms episode-mean P95, but is host-specific.Emergency fallback can violate the robust constraint.Source: §2.8 · pp. 12–13
  • Figure 6 traces residuals, margins, candidate counts, actions, and predicted versus actual safety margins; it is descriptive and does not imply fallback preserves safety..Source: Figure 6 · p. 13

2.9. One-factor sensitivity sweep

The sensitivity sweep varies one configuration factor at a time and selects configurations using development data; the companion fallback analysis provides an exact cause breakdown only under its registered scalar ACC model and tolerance.

2.9. One-factor sensitivity sweep

  • The test endpoint was unchanged across the one-factor configurations in this cohort, while projection, fallback, correction, and jerk differences were retained for analysis.Development ranking used safety, then violation rate, action correction, and jerk; independent test rows were not used for selection.Source: §2.9 · p. 13

2.10. Fallback causes and outcomes

  • Under the registered scalar one-step ACC model and −10−8 tolerance, Adaptive RACF had 1,241 fallback invocations: 808 feasible-set-empty, 433 solver-failure, and zero post-check-failure.This exactness statement is not a generic RACF or closed-loop safety guarantee.Source: §2.10 · p. 13

3. ADDITIONAL EVIDENCE AND REPRODUCIBILITY

The additional evidence separates cohorts and mechanisms, reports matched comparisons of safety and computation, and tests how far the theoretical premises are supported. The appendix also specifies adaptive execution and baseline contracts, while documenting limits on empirical and theoretical conclusions.

3.1. Evaluation cohorts and data sources

  • The residual-margin isolation and registered comparison use distinct cohorts with different job sources and Static counts, and their trial-key sets are unverified, so the rows are not pooled.The package includes protocols, manifests, source hashes, and documentation of the cohort distinction.Source: §3.1 · p. 14

3.2. Matched-window mechanisms and computation

  • In the matched-window study, Robust reaches 171/180 safe episodes versus Adaptive’s 158/180, while Adaptive’s difference from Fixed is −2.22 pp with a 95% interval spanning zero.Floor activation raises coverage but produces zero discordant safety pairs; the authors describe this as an observed null, not population equivalence.Source: §3.2 · p. 14
  • Adaptive averages 2.434 ms per executed step versus Robust’s 3.090 ms, with 161/180 versus 170/180 safe episodes; the rollouts are partial, not a closed-loop certificate or external benchmark.The runtime measurement includes setup, inference, filtering, updates, simulation, diagnostics, and outcome aggregation, but excludes checkpoint loading and trace compression.Source: §3.2 · pp. 14–15
  • Adaptive RACF exceeds ACI by 5.21 pp and CPSF-style by 5.50 pp on the shared cohort; their policies, reset states, lead trajectories, solver, and fallback are unchanged.Against Envelope and Robust, the reported paired intervals show trade-offs across safety, projection, correction, and jerk.Source: §3.2 · p. 15

3.3. Limitations and negative results

  • Candidate-only matches Static at 144/180 safe episodes, while margin-only and Joint each reach 161/180; Adaptive and Envelope safety remains empirical because they relax formal premises.ACI and CPSF-style are one-step interface comparisons, not reproductions of multi-step viability filters.Source: §3.3 · p. 15

3.4. Assessment of theoretical assumptions

  • The aligned trace check verifies structural premises on 90,000 steps but does not establish the exchangeability or deployment-TV inputs, and fallback includes steps with negative robust constraints.The trace analysis reports zero violations when residual coverage and the nominal premise both hold, but does not estimate IID/TV assumptions or a closed-loop guarantee.Source: §3.4 · p. 15

3.5. Adaptive execution order

  • Grade filtering precedes projection; completed-transition margin and selector updates affect the next step, with selection starting after 20 transitions and recomputed every ten.Selection uses a 40-transition window; an upward crossing of 2qα restores the full grid for 20 completed transitions and suspends pruning during recovery.Source: §3.5 · p. 15

3.6. Reproducibility and baseline contracts

  • The reproducibility materials define the four-condition, two-scenario, 25-reset matrix and the ACI and CPSF-style interfaces; figures and tables cover registered slices and safety–utility comparisons.Episode safety requires nonnegative headway margin and no collision, while utility uses observed prefixes, so Raw collisions confound cross-method utility comparisons through survival/truncation.Source: §3.6 · p. 15, Figure 10 · p. 16, Table 14 · p. 16

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