Adaptive Stress Testing with Reward Augmentation for Autonomous Vehicle Validation

Anthony Corso; Katherine Driggs-Campbell; Mykel J. Kochenderfer; Peter Du

REVIEW 3 major objections 5 minor 16 references

Adaptive Stress Testing with Reward Augmentation for Autonomous Vehicle Validation

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read By augmenting the Adaptive Stress Testing reward with Responsibility-Sensitive Safety and trajectory-dissimilarity terms, this paper shows that simulation-based failure search can recover a broader, more relevant set of autonomous-vehicle…

desk verdict Practical AST reward tweaks with a plausible RSS demonstration, but the diversity claim needs repeated-seed evidence before it can be taken literally. read the letter →

arxiv 1908.01046 v2 pith:PE4A4JVH submitted 2019-08-02 cs.RO cs.AIcs.LGcs.SYeess.SYstat.ML

Anthony Corso , Peter Du , Katherine Driggs-Campbell , Mykel J. Kochenderfer This is my paper · ORCID

classification cs.ROcs.AIcs.LGcs.SYeess.SYstat.ML

keywords AdaptiveStressTestingautonomousvehiclevalidationrewardaugmentationReinforcementLearningResponsibility-SensitiveSafetytrajectorydissimilarityfailurescenariosearchsimulation-based

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Adaptive Stress Testing (AST) searches for likely failure scenarios of an autonomous vehicle by framing the scenario search as a Markov decision process and solving it with reinforcement learning. The paper's claim is that AST alone concentrates on collisions the vehicle cannot avoid and keeps rediscovering the same failure mode, so the authors modify the reward function in two ways: they use Responsibility-Sensitive Safety (RSS) rules to reward collisions in which the vehicle behaved improperly, and they add a trajectory-dissimilarity term that rewards each new failure for being unlike failures already found. In a simulated crosswalk scenario, these augmentations produce a wider and more useful set of failures: with the RSS reward, nearly all collisions involve a nontrivial fraction of improper vehicle responses, and with the dissimilarity reward, the search finds vehicle-caused pedestrian collisions and vehicle-vehicle collisions that the generic reward never found. If correct, this gives validation engineers a way to turn simulation testing toward the failure modes that actually reveal policy weaknesses.

What carries the argument

The load-bearing object is the augmented reward function of the AST Markov decision process. Generic AST gives $R(s)=0$ for a critical state, $-\alpha-\beta D(r_v,r_p)$ when the episode times out without a collision, and $-M(a|s)$ during the episode, where $M$ is the Mahalanobis distance penalizing unlikely environment actions. The RSS augmentation replaces the critical set with $E_\mathrm{RSS}=\{\tau \mid \tau\in E,\ f_\mathrm{imp}(\tau)>f_\mathrm{crit}\}$ and replaces the terminal distance term with a penalty proportional to the fraction of improper timesteps, biasing the solver toward collisions the vehicle could have avoided. The trajectory-dissimilarity augmentation rewards a failure trajectory with $\frac{\gamma}{\mu}\sum_i D(\tau_s,\tau_i)$, where $D$ averages the Euclidean distance between $n$ normalized segment centers of mass of the new trajectory and each previously returned failure trajectory, so the solver is pushed away from failure modes it has already found. These two mechanisms, alone or in combination, are what carry the argument that reward augmentation changes the discovered failure space.

What would settle it

Run a dense uniform random search over the same environment-action space in the same simulator and count how often the vehicle-induced pedestrian collisions and vehicle-vehicle collisions occur. If those modes appear at comparable rates under random search, then the augmented-reward result is a statement about search efficiency rather than about the existence of a larger failure space; if they never appear, the claim that these are genuine failures of the AV policy would need to be re-examined.

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Extended reading notes

Core claim

The central discovery, stated on the paper's own terms, is that the reward function in AST controls not only whether failures are found but which failures are found, and that domain knowledge can be injected through that reward to make the search return failures that matter. The RSS augmentation restricts the critical set to trajectories whose fraction of improper vehicle timesteps, $f_\mathrm{imp}(\tau)$, exceeds a threshold $f_\mathrm{crit}$, and uses $\beta f_\mathrm{imp}(\tau)$ as the penalty for trajectories that do not reach that set; in the single-pedestrian TRPO experiment, the trajectories found by this reward have substantially higher improper-response fractions than those found by generic AST. The trajectory-dissimilarity augmentation changes the reward for reaching the critical set to $\frac{\gamma}{\mu}\sum_{i=1}^{\mu} D(\tau_s,\tau_i)$, the average dissimilarity between the new failure trajectory and previously found failures, where $D$ is computed from normalized segment centers of mass. In the two-vehicle, two-pedestrian MCTS experiment, generic AST returned 25 failures, all pedestrian-induced collisions with a stopped vehicle, while the dissimilarity-augmented reward returned 15 pedestrian-induced collisions, 4 vehicle-induced vehicle/pedestrian collisions, and 6 vehicle/vehicle collisions, showing a larger and more expressive subset of the failure space.

Load-bearing premise

The RSS reward depends on the assumption that the chosen Responsibility-Sensitive Safety rules and parameters—including a zero response time and the specified acceleration bounds—correctly say when the autonomous vehicle is to blame in a collision; if that responsibility label is wrong, the 'relevant' failures it highlights are mislabeled and no more useful than the generic ones.

Editorial extensions

If this is right

Validation runs with AST can now report a portfolio of failures across multiple modes, so an engineer learns about several weaknesses in one campaign rather than one repeated weakness.
Failures found with the RSS reward are more likely to be cases where the autonomous vehicle's own behavior is blameworthy, which points directly at places where the driving policy needs improvement.
The trajectory-dissimilarity term can be applied to any black-box simulator that exposes trajectories, so the diversity mechanism is not tied to the specific crosswalk scenario.
The number of failures returned by AST is an incomplete measure of validation value; the distribution of failure types and their responsibility classification matters as much as the count.
Combining the RSS and dissimilarity rewards in one framework should, if the paper's mechanism is right, yield a set of failures that is simultaneously diverse and vehicle-induced, which is the natural next step the authors identify.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A testable extension the authors leave implicit is to apply the RSS reward to label the other agents' behavior as well as the AV's, so AST could be used to find failures caused by pedestrians or other vehicles, not only failures the AV should have prevented.
The fixed coefficient $\gamma$ in the dissimilarity reward could be annealed over the search horizon; a time-varying weight would let the solver first explore broadly and then concentrate on separating the most similar remaining failure modes, which the paper's constant-weight setup does not address.
The paper measures diversity by spatial trajectory shape; a complementary metric would define diversity by failure mechanism (sensor-noise-induced versus control-induced), which might correlate more directly with which subsystem of the autonomy stack needs fixing.
Because the RSS parameters (including $\rho=0$ and the chosen acceleration bounds) are simulator-specific, a practical deployment would need to calibrate them to the actual vehicle and pedestrian dynamics; the set of 'relevant' failures will shift if those parameters change.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

One thing you should know: this is a modest, well-scoped paper. It takes the AST framework and adds two reward terms—one based on RSS responsibility classification, one based on trajectory dissimilarity—to push AST toward failures where the AV is at fault and toward a more varied set of failures. The RSS experiment is the stronger half. The trajectory diversity experiment is the weaker half: the central claim that generic AST discovers zero vehicle-induced or vehicle-vehicle failures comes from what looks like a single MCTS run, and that needs replication.

What's new: the specific combination. RSS has been used for responsibility rules before; trajectory dissimilarity is borrowed from Liu and Schneider. Putting them into the AST reward is a straightforward but reasonable engineering move. The paper is clearly written, the experimental setup is described well enough to reproduce, and the qualitative trajectory examples in Figures 5 and 6 make the RSS effect vivid. The authors also note that RSS parameters should be chosen with care, which is honest.

The RSS results show a large shift in the f_imp histogram, and that shift is plausible even without error bars. The TD results are where I'd push back. In Table III, the zero counts are load-bearing, and a single run of MCTS is not enough to establish that generic AST 'did not discover' those failure types. It could just be an unlucky seed. Also, the TD reward explicitly maximizes trajectory dissimilarity, so the finding that TD produces more diverse trajectories is partly baked in. The categorical breakdown (vehicle-induced VP, vehicle/vehicle) is the independent evidence, but that evidence needs statistical grounding. I would like to see multiple seeds, confidence intervals, and maybe a sensitivity analysis for gamma and n. The RSS parameter assumption is a secondary concern; it's a modeling choice and the authors flag it.

Who is this for: people actively working on AST or simulation-based AV validation. It's not a breakthrough, but it's a useful practical tweak. I think it deserves peer review—the idea is testable and the claim matters—but it should come back with repeated-seed data. Without that, the strong wording of the diversity claim should be softened.

Referee Report

3 major / 5 minor

Summary. The paper addresses a known limitation of Adaptive Stress Testing (AST) for autonomous vehicle validation: generic AST tends to find unavoidable collisions and repeatedly discovers similar failure modes. The authors propose two reward augmentations: (1) an RSS-based reward that gives zero terminal reward only to collisions where the vehicle's trajectory has an improper fraction above a threshold fcrit, and (2) a trajectory dissimilarity reward that adds a bonus proportional to the average distance between a new failure trajectory and previously found top failures. They evaluate the RSS augmentation with TRPO in a single-pedestrian crosswalk scenario, reporting a shift in the distribution of the improper-timestep fraction, and evaluate the dissimilarity reward with MCTS in a two-vehicle/two-pedestrian scenario, reporting counts of failure types in Table III. The authors conclude that augmented AST discovers a larger and more expressive subset of the failure space compared with generic AST, and that these failures are more relevant for validating an autonomous vehicle policy.

Significance. If the empirical claims hold, this is a practical and useful contribution. The paper clearly identifies a genuine bottleneck of AST (mode collapse and discovery of unavoidable collisions) and proposes two well-motivated, easy-to-implement reward modifications. The specific new failure types in Table III (vehicle-induced vehicle/pedestrian and vehicle/vehicle failures) are exactly the kinds of outcomes that matter for AV validation, and the paper states a falsifiable empirical prediction: the augmented reward will discover failure modes that generic AST does not. The manuscript does not provide formal guarantees, machine-checked proofs, or a code release, but the method description is sufficiently detailed to reimplement. The main weakness is statistical: the headline comparison rests on a single run per condition, and the quantitative claims are partly evaluated using metrics that are also the optimized objectives.

major comments (3)

[Section IV-B, Table III] The strongest claim in the paper, that generic AST 'did not discover' vehicle-induced vehicle/pedestrian or vehicle/vehicle failures, rests on counts that appear to come from a single MCTS run per reward condition. AST is stochastic: MCTS uses random rollouts and the policies or tree statistics are randomly initialized. A single run cannot establish that generic AST produces zero failures of those types. Please repeat the experiment over multiple seeds and report means with confidence intervals, or apply a statistical test (e.g., a Poisson or bootstrap comparison) to the failure-type counts. If repeated runs yield nonzero counts for generic AST, the conclusion must be softened from 'did not discover at all' to 'discovered significantly less frequently.' This is load-bearing because the abstract and Section V directly claim a larger and more expressive subset of the failure space.
[Section IV-A, Figure 4 and Eq. (6)] The RSS reward directly optimizes the fraction of improper timesteps fimp: the terminal reward is zero only if fimp exceeds fcrit, and the non-terminal penalty is proportional to fimp. Observing that RSS-augmented AST produces trajectories with higher fimp is therefore partly a consequence of the objective rather than independent evidence of improved relevance. To support the claim that these failures are 'more useful,' evaluate relevance with a measure not contained in the reward, such as an independent avoidability label, human expert judgment, or a quantitative metric of whether the vehicle could have acted differently. In addition, Figure 4 shows aggregate histograms without error bars or a statistical comparison; statements such as 'the most common type of failure involves vehicle trajectories where the vehicle is not at fault' are not supported without repeated trials and a quantitative comparison.
[Section III, Table I] The reported results depend on several free parameters that are not analyzed: fcrit, gamma, n, alpha, beta, and the RSS parameters in Table I (rho = 0 and the chosen acceleration bounds). These choices directly determine which trajectories are classified as improper and how much weight is placed on diversity. In particular, rho = 0 and the acceleration bounds are plausible but not validated, and the paper itself notes that 'for industrial applications, these parameters should be chosen with care.' A sensitivity analysis, or at least a discussion of how the qualitative conclusions change with these parameters, is needed to support the generality of the contribution. The stated assumption in Section III-A that higher fimp implies higher likelihood of collision is also asserted rather than tested; please provide evidence for this correlation or soften the claim.

minor comments (5)

[Section II-B, Eq. (3)] The displayed formula for the head-on safe longitudinal distance contains ambiguous notation ('v1 +v1,rho 2 rho' appears to be a typesetting error); please re-typeset it so that the product terms are clear and consistent with the definitions of v1,rho and v2,rho.
[Section IV-B, Table III] The decrease in pedestrian-induced failures from 25 (generic) to 15 (TD reward) is not discussed. Since the dissimilarity reward changes the composition of the returned set, a short discussion of this trade-off would help readers understand whether the augmentation sacrifices coverage of one failure mode to gain another.
[Section IV-B] The paper states that the MCTS solver is run for 'the same number of iterations' but does not report the number of iterations, the UCT exploration constant, the rollout policy, or the TRPO network architecture and training hyperparameters. Please include these details for reproducibility.
[Section IV-A, Figure 4] Consider presenting the fimp distributions as normalized empirical CDFs or as histograms with bin counts and error bars, rather than smoothed density curves, so that the comparison between the generic and RSS-augmented conditions is more quantitative and easier to assess.
[Abstract and Section V] The phrases 'more expressive subset of the failure space' and 'relevant failures' are used without operational definitions. Adding a precise definition of expressiveness and a criterion for failure relevance would sharpen the claims and make them testable.

Circularity Check

2 steps flagged · score 6.0 of 10

RSS and TD evaluations reuse the exact quantities inserted into the reward; categorical failure modes provide partial independence.

self definitional [Section III-A, Eqs. (5)-(6); Section IV-A, Fig. 4]
"We define fimp as the fraction of timesteps considered improper by RSS for the state trajectory of the autonomous vehicle. The set of critical events E is altered to only include events that result from trajectories where the AV has behaved improperly. ... RRSS(s) = 0 s∈ERSS; -α-βfimp(τ) s∉ERSS,t≥T. ... For the RSS reward function, all trajectories have a non-zero fraction of improper timesteps, and in most trajectories, the AV policy behaved improperly for more than 25% of the simulation timesteps."

The RSS-augmented reward explicitly contains -β fimp, so the RL solver is directly rewarded for maximizing fimp, the same quantity later reported as the main evidence of finding 'relevant' failures. In addition, the critical set is redefined by Eq. (5) to contain only trajectories with fimp > fcrit, so any discovered failure must, by construction, have a positive improper fraction. The observation that RSS-augmented AST yields high fimp is therefore a direct consequence of the objective, not an independent finding. The only independent content is whether these fimp-defined failures are indeed more 'relevant' in an external sense, which is not separately evaluated.
self definitional [Section III-B, Eq. (8); Section IV-B, Fig. 8 and Table III]
"The reward function is then modified as follows RTD(s) = γ/μ ∑_{i=1}^{μ} D(ts,ti) for s∈E. ... By incorporating the dissimilarity metric, the solver is able to explore a larger subset of the failure space. Table III shows that the trajectories obtained now consist of other failure modes in addition to the pedestrian induced ones discovered using the generic AST reward function."

Equation (8) gives a positive reward proportional to the sum of trajectory-dissimilarity values D(ts,ti) between the current trajectory and previously found top failures. The solver is therefore explicitly selecting trajectories to maximize the same dissimilarity-based diversity metric that the paper then reports as evidence of a 'larger and more expressive subset of the failure space.' The categorical breakdown in Table III is not identical to D and provides some independent signal, but the returned set is generated and ranked under the TD objective, so the headline diversity result is substantially forced by the reward definition.

full rationale

Two evaluation claims in the paper reduce, at least in part, to the reward definitions. First, the RSS reward inserts fimp into the objective and redefines failures to require fimp > fcrit, so finding trajectories with high improper-response fractions is guaranteed by construction; the paper then uses this same fimp distribution as evidence of finding 'relevant' failures. Second, the TD reward directly rewards trajectory dissimilarity D, and the paper reports increased diversity as a central success; this is the selected objective, not an independent outcome. However, the paper also reports categorical failure types (vehicle-induced vehicle/pedestrian, vehicle/vehicle) in Table III, which are not directly encoded in the TD reward, and the RSS qualitative example in Fig. 6 demonstrates a specific improper-braking failure mode that is meaningfully different from the generic AST result. These categorical and qualitative results give the central claim some independent empirical content. The self-citations in the paper are to baseline AST work and are not load-bearing for the new augmentation claims. The single-run, no-confidence-interval issue noted by the skeptic is a correctness/robustness concern, not a circularity concern, and does not affect this score.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim rests on several hand-chosen free parameters (reward constants, RSS thresholds, diversity weight, segment count, RSS physical parameters) and on domain assumptions about AST, RSS, and the representativeness of the simulation. No entirely new physical or conceptual entities are introduced.

free parameters (6)

α (collision penalty constant) = 10000
Chosen by hand to penalize non-failure trajectories; not fitted to data.
β (distance penalty constant) = 1000
Chosen by hand to weight the Euclidean distance term; not fitted to data.
fcrit (RSS improper timestep threshold) = not specified
Tunable parameter governing how many improper timesteps are required for a failure to be considered at fault; value not reported in experiments.
γ (diversity reward weight) = not specified
User tunable parameter controlling how much the solver is rewarded for diverse failures; value not reported in experiments.
n (number of trajectory segments) = not specified
Predefined constant for trajectory normalization in the dissimilarity metric; value not reported.
RSS parameters (ρ, a_acc_max, a_brk_min, a_brk_max) = ρ=0, a_acc_max=0.1g, a_brk_min=0.05g lateral and 0.7g longitudinal, a_brk_max=0.7g
Chosen by authors to approximate plausible accelerations; explicitly noted that parameter choice affects discovered failures.

assumptions (4)

domain assumption AST formulation as an MDP and the use of RL solvers correctly find the most likely failures of the system-under-test.
Taken from prior work (Lee et al. 2015, Koren et al. 2018) and assumed without justification in this paper.
domain assumption The RSS model is a correct formalization of safe driving responsibilities and can be applied to the pedestrian-vehicle interaction.
The paper uses RSS rules as a ground truth for proper and improper behavior, but does not validate RSS on the specific scenario.
ad hoc to paper Trajectories with a higher fraction of improper timesteps are more likely to end in a collision (Section III-A).
This assumption is stated explicitly by the authors to justify the RSS reward design.
domain assumption The simulated crosswalk scenario with IDM vehicle control is representative of real autonomous vehicle validation needs.
The paper uses a single simplified scenario and does not discuss transferability to other scenarios.

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Cite this review

Pith. "Pith review of Adaptive Stress Testing with Reward Augmentation for Autonomous Vehicle Validation." pith.science (2026). https://pith.science/paper/PE4A4JVH

@misc{pith2026190801046,
  author       = {Pith},
  title        = {Pith review of: Adaptive Stress Testing with Reward Augmentation for Autonomous Vehicle Validation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PE4A4JVH}},
  note         = {Machine review of arXiv:1908.01046}
}

read the original abstract

Determining possible failure scenarios is a critical step in the evaluation of autonomous vehicle systems. Real-world vehicle testing is commonly employed for autonomous vehicle validation, but the costs and time requirements are high. Consequently, simulation-driven methods such as Adaptive Stress Testing (AST) have been proposed to aid in validation. AST formulates the problem of finding the most likely failure scenarios as a Markov decision process, which can be solved using reinforcement learning. In practice, AST tends to find scenarios where failure is unavoidable and tends to repeatedly discover the same types of failures of a system. This work addresses these issues by encoding domain relevant information into the search procedure. With this modification, the AST method discovers a larger and more expressive subset of the failure space when compared to the original AST formulation. We show that our approach is able to identify useful failure scenarios of an autonomous vehicle policy.

Figures

Figures reproduced from arXiv: 1908.01046 by the authors.

**Figure 1.** In these plots, the vehicle moves from left to right and [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Example trajectory with the danger classification at each timestep. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

Figures from the paper (6 more)

**Figure 3.** Figure 3: Example trajectory with autonomous vehicle response classification [PITH_FULL_IMAGE:figures/full_fig_p003_3.png]

**Figure 4.** Figure 4: Distribution of trajectories over fraction of improper response for [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: Example trajectory with the generic AST reward. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: Example trajectory with RSS reward augmentation. [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

**Figure 7.** Figure 7: Trajectories returned with generic AST reward (two pedestrian/two [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

**Figure 8.** Figure 8: Trajectories returned with TD reward augmentation (two pedes [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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G. E. Mullins, P. G. Stankiewicz, R. C. Hawthorne, and S. K. Gupta, “Adaptive Generation of Challenging Scenarios for Testing and Evaluation of Autonomous Vehicles,”Journal of Systems and Software , vol. 137, pp. 197–215, 2018

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