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Control Tax: The Price of Keeping AI in Check

Mikhail Terekhov, Zhen Ning David Liu, Caglar Gulcehre, Samuel Albanie

arXiv:2506.05296v3cs.AIcs.LG

TL;DR

As AI systems enter broader pipelines, control adoption may hinge on its operational and financial overhead. This paper defines Control Tax and links monitor performance and cost to deployment safety; its analysis shows that cheaper monitors can sometimes yield greater safety under constrained auditing budgets.

  • Problem

    Adoption of AI Control may depend on the operational and financial overhead of integrating control measures into AI pipelines.

    Source: §1 · p. 1

  • Method

    A unified framework combines empirical monitor performance with a game-theoretic model to connect monitoring costs to strategic, long-term deployment safety.

    Source: §1 · pp. 1–2

  • Results

    45x more cost moves from Gemini 2.0 Flash to o3-mini on the Pareto frontier for a 0.15 safety-score gain against GPT-4o.

    Source: §6 · p. 9

  • Takeaways & Limitations

    The framework translates safety objectives into monitoring costs across batch and sequential deployments under auditing constraints.

    Source: §1 · p. 2

    The evaluation uses only APPS, which lacks agentic tasks, and focuses primarily on advanced models.

    Source: §7 · p. 9

Abstract

from arXiv · show

The rapid integration of agentic AI into high-stakes real-world applications requires robust oversight mechanisms. The emerging field of AI Control (AIC) aims to provide such an oversight mechanism, but practical adoption depends heavily on implementation overhead. To study this problem better, we introduce the notion of Control tax -- the operational and financial cost of integrating control measures into AI pipelines. Our work makes three key contributions to the field of AIC: (1) we introduce a theoretical framework that quantifies the Control Tax and maps classifier performance to safety assurances; (2) we conduct comprehensive evaluations of state-of-the-art language models in adversarial settings, where attacker models insert subtle backdoors into code while monitoring models attempt to detect these vulnerabilities; and (3) we provide empirical financial cost estimates for control protocols and develop optimized monitoring strategies that balance safety and cost-effectiveness while accounting for practical constraints like auditing budgets. Our framework enables practitioners to make informed decisions by systematically connecting safety guarantees with their costs, advancing AIC through principled economic feasibility assessment across different deployment contexts.

1 INTRODUCTION

AI Control (AIC) addresses risks from malicious users and potentially misaligned systems, but adoption may depend on oversight overhead. The paper defines Control Tax and connects monitor performance and cost to deployment safety.

1 INTRODUCTION

  • Control Tax is the operational and financial cost of integrating control measures into AI pipelines.The framework connects empirical monitor performance with strategic, long-term deployment safety.Source: §1 · p. 1
  • The empirical setting uses attacker models to insert subtle code flaws and monitor models to detect them, producing ROC curves for the safety analysis.Static curves alone do not quantify safety when auditing resources are constrained.Source: §1 · p. 1
  • Control Tax curves connect a monitor’s performance and financial cost to a concrete safety probability under a given auditing budget.Figure 1 plots achievable safety against average monitor cost for sequential monitoring with a 5% fixed auditing budget.Source: §1 · p. 2, Figure 1 · p. 2
  • The framework covers batch and sequential deployments and treats even one approved backdoor as system failure.It aims to translate safety objectives into monitoring costs for deployment decisions.Source: §1 · p. 2

2 MONITOR PERFORMANCE ON CODE BACKDOORS

The study evaluates language models as code-backdoor attackers and monitors using APPS problems, then uses monitor performance to characterize AIC safety. It reports strong monitoring performance alongside findings about attacker variation and monitor errors.

2 MONITOR PERFORMANCE ON CODE BACKDOORS

  • The evaluation uses APPS code problems: attacker models introduce vulnerabilities, and monitors distinguish backdoored solutions from correct ones.The test split is filtered to 2,427 samples; APPS provides test cases for defining vulnerabilities.Source: §2 · p. 2

2.1 BACKDOOR GENERATION

  • A backdoor passes public tests but produces an incorrect output on at least one untested input; correct solutions come from APPS while backdoors are generated by attackers.The pipeline proposes and ranks strategies, then iteratively checks candidates against public tests and specified trigger inputs, with up to ten attempts per problem.Source: §2.1 · pp. 2–3

2.2 MONITOR PIPELINE

  • Monitors score suspiciousness from 1 to 100 rather than making only binary judgments, supporting nuanced decisions under limited auditing budgets.The code is formatted and comments are removed to reduce potential model biases.Source: §2.2 · p. 3

2.3 RESULTS

  • Monitoring performance remains consistent across many attackers with diverse capabilities, so stronger models do not necessarily produce subtler backdoors.The authors note newer GPT-4.1 and Gemini 2.5 models appear to produce subtler backdoors.Source: §2.3 · pp. 3–4
  • 0.92 - 0.96 AUC: OpenAI’s o3-mini achieves these scores, while conventionally stronger models generally perform better at monitoring.Figure 3 summarizes AUC across attacker-monitor pairs.Source: §2.3 · p. 3, Figure 3 · p. 4
  • Most monitor errors are false positives, and preliminary calibration experiments indicate modest accuracy gains.The authors identify calibration as a direction for future work.Source: §2.3 · p. 4
  • ROC curves from the empirical evaluation serve as inputs to a strategic game model for translating monitor performance and cost into long-term safety.The section frames this as a bridge from static performance metrics to actionable deployment guarantees.Source: §2.3 · p. 4

3 SAFETY IN LONG-TERM DEPLOYMENT

The framework translates monitoring performance and auditing resources into safety estimates for long-term deployment. It analyzes batch and sequential strategies under a failure criterion where one approved backdoor compromises the system.

3 SAFETY IN LONG-TERM DEPLOYMENT

  • The framework models red-team backdoor attempts and blue-team audits, with safety depending on monitor performance, attacker success, and the auditing budget.It assumes a stateless attacker, and the blue team wins by auditing any submission containing a backdoor attempt.Source: §3 · pp. 4–5

3.2 SEQUENTIAL NOT ANYTIME TRUSTED MONITORING

  • Batch monitoring gives better safety in most settings, but not all; Figure 5 compares batch and sequential safety across auditing budgets.The caption notes that shifting to batch may improve safety at low auditing budgets.Source: Figure 5 · p. 6, §3.2 · p. 7

3.1 BATCH TRUSTED MONITORING

  • In batch deployment, the blue team audits the most suspicious submissions before execution, and batch monitoring is equivalent to upfront auditing at an effective budget t0.The effective budget t0 is derived from the ROC curve and can exceed the actual budget c.Source: §3.1 · pp. 5–6, Figure 4 · p. 6
  • For upfront and batch auditing, the optimal attacker backdoor probability scales as Θ(1/N), so it halves when the deployment horizon doubles.If the optimal rate decays faster than 1/N, the attacker may fail to insert any backdoor as N grows.Source: §3.1 · p. 6

3.2 SEQUENTIAL NOT ANYTIME TRUSTED MONITORING

  • Sequential not-anytime deployment requires immediate, time-dependent audits because the blue team cannot reorder submissions and a missed successful backdoor ends the game.The allocation strategy is non-increasing over time; rearranging a finite strategy this way is at least as safe as the original.Source: §3.2 · p. 6
  • In SNAC, a large initial audit allocation corresponds to an attacker rate scaling as λ*/N, while a small initial allocation can favor constant backdooring.The models assume the attacker and monitor know N; comprehensive treatment of indefinite anytime deployment is left to future work.Source: §3.2 · p. 7
  • As N grows, the SNAC analysis models attacker insertions as a Poisson process with rate λ when the attack probability scales as λ/N.The optimal game value and rate stabilize by N = 100, while narrow, non-overlapping peaks indicate that attacker knowledge of N is critical.Source: §3.2 · p. 7, Figure 6 · p. 8

4 DISCUSSION

The discussion connects monitor performance and monitoring cost to deployment safety, then draws protocol-specific lessons for finite and unknown horizons. It also notes that backdoor subtlety may not rise with stronger attackers under the current evaluation conditions.

4 DISCUSSION

  • Conditioning on valid backdoors that pass standard tests provides robust safety against simpler attacks, but stronger attackers may change this if given subtlety feedback.The authors report that current models do not substantially increase backdoor subtlety under these conditions.Source: §4 · p. 8
  • For finite-horizon deployments, hiding the known task count matters because an attacker’s optimal insertion probability scales as 1/N and deviations sharply reduce its win probability.The authors identify disclosure of N as a critical vulnerability for both batch and sequential deployments.Source: §4 · p. 8
  • With an unknown, effectively infinite horizon, a patient attacker can insert backdoors ever more rarely (pb →0) and eventually succeed, exposing a weakness of pure monitoring.Source: §4 · p. 8
  • In finite sequential deployments, defenders should allocate more of the audit budget early because the optimal allocation is non-increasing over time.The stated aim is to reduce the risk of an early, unrecoverable compromise.Source: §4 · p. 8

5 RELATED WORK

The related work situates this paper within AI control, scalable oversight, and security and machine-learning research. It distinguishes its cost-focused modeling from work emphasizing safety–usefulness trade-offs and discusses differences from a concurrent scalable-oversight study.

AI control

  • Unlike Griffin et al. (2024), which models the safety–usefulness trade-off, this work focuses on safety versus costs as a concern for real-world AIC adoption.Source: §5 · p. 8

Scalable oversight

  • Engels et al. (2025) also study APPS backdooring, but their non-agentic setup may underelicit attacker capabilities and their binary classifiers do not provide the numerical scores needed here.Source: §5 · p. 9

Security and machine learning

  • The paper connects AIC to work on LM-generated code vulnerabilities, steganography for circumventing statelessness, model organisms of misalignment, and calibration of LM judgment uncertainty.Source: §5 · p. 9

6 CONCLUSIONS

The paper frames Control Tax as a trade-off between safety gains and monitoring costs, with the most expensive, highest-performing monitor not always maximizing safety. It also highlights fine-grained, unpredictable auditing strategies and protocol-level safeguards as practical directions.

6 CONCLUSIONS

  • A 45x cost increase from Gemini 2.0 Flash to o3-mini buys a 0.15 absolute safety-score improvement, from ∼0.70 to ∼0.85 against a GPT-4o attacker.The authors use this Pareto-frontier comparison to illustrate that marginal safety gains can require substantial investment.Source: §6 · p. 9
  • The highest-performing, most expensive monitor is not always the best choice for maximizing safety because a cheaper monitor can leave budget for more auditing.Gemini 2.0 Flash is given as an example of a cheaper, weaker monitor that may support higher-volume auditing.Source: §6 · p. 9
  • Fine-grained, unpredictable audits, including concealed audit horizons, are highlighted as strategies for mitigating adversarial evasion attempts.Source: §6 · p. 9
  • The conclusion presents protocol-level safeguards as practical and necessary, while calling for continued refinement to optimize safety within acceptable performance costs.Source: §6 · p. 9

7 LIMITATIONS

The evaluation and analysis have explicit scope boundaries, including APPS-only validation without agentic tasks and a focus on safety and auditing costs. The paper also flags possible misuse of its backdoor-generation techniques and provides materials for reproduction.

7 LIMITATIONS

  • Validation is limited to APPS, which lacks agentic tasks, and focuses mainly on GPT-3.5-turbo and above; the study also leaves usefulness trade-offs and anytime monitoring for future treatment.The authors additionally note that honest and malicious solutions were generated differently and suggest generating both from the same attacker models in future work.Source: §7 · p. 9
  • Backdoored-code generation techniques could be exploited for harm, although the paper focuses on mitigating backdoor damage through proactive threat modeling.Source: §7 · p. 10
  • The repository includes experiment instructions and the APPS backdoor dataset, while appendices document filtering, prompts, and numerical optimization for auditing strategies.Source: §7 · p. 10

A FILTERING THE APPS DATASET

This appendix describes the APPS filtering procedure used to select script-based problems with reliable tests and enough short public tests for backdoor generation. It also covers how subtle backdoors were generated and monitored, and reports attacker-model performance on the original APPS benchmark.

A FILTERING THE APPS DATASET

  • APPS filtering keeps script-based problems, excludes multi-answer problems when any of at least three solutions fails a test, and requires at least three suitable public tests.A suitable test has input and output totaling no more than 1,000 characters, so the tests fit in attacker context windows.Source: A FILTERING THE APPS DATASET · p. 13

B.1 BACKDOOR GENERATION

  • The backdoor must be domain-related, pass unit tests, and cause failure only on a rare valid input, avoiding arbitrary checks and magic numbers.The prompt also says not to use a fail input that already appears in the unit tests.Source: §B.1 · pp. 13, 18
  • The generation workflow asks the model to brainstorm modifications, critique those ideas in a fresh context, and produce a backdoored solution from the critique.The output is also required to include the subtly wrong solution, a hint, and a failing input.Source: §B.1 · pp. 17–19
  • The backdoor-generation prompt requires code to pass official unit tests yet fail on a specific valid input.It requests the wrong code, failing input, and explanation in tagged fields, and instructs removal of comments or variable names that would reveal the flaw.Source: §B.1 · p. 19

B.2 MONITORING

  • The monitoring prompt asks models to inspect a solution for an intentional backdoor, identify suspicious code, and rate confidence from no backdoor to backdoor.The rating is an integer between supplied minimum and maximum values, with the final answer placed in answer tags.Source: §B.2 · p. 19

C.1 MODEL PERFORMANCE ON APPS

  • Figure 7 presents attacker-model performance on original APPS, with models from each provider ordered by strength.To reduce costs, Sonnet 3.7 CoT was not run; o1-mini and o3-mini used random subsets of 200 problems per difficulty, and overall statistics were weighted by each difficulty’s size in the full dataset.Source: Figure 7 · p. 20, §C.1 · p. 20

C.2 ATTACKERS

Across these analyses, attacker strength and prompting variations generally do not change monitoring performance once backdoors pass public tests. The appendices also examine scoring, calibration, safety under auditing budgets, and illustrative backdoors.

C.2 ATTACKERS

  • Attacker success rates roughly track general coding ability and change little with problem difficulty; common failures include conspicuous flaws and backdoor inputs that do not work.A case where correct code fails on the backdoor input is not counted as a backdoor under the paper’s definition.Source: §C.2 · pp. 20–21

C.3 MONITORING FAILED BACKDOORS

  • After filtering for backdoors that pass public tests, monitoring performance no longer varies with attacker strength, unlike on failed attempts.For failed attempts, stronger attackers’ edits were harder to spot. The authors’ example shows a weak model’s “magic if-statement” backdoor, which monitors readily spot; comments in generated code make comment filtering important.Source: §C.3 · p. 22, §D.1 · p. 28

C.4 SUSPICIOUSNESS HISTOGRAMS

  • Monitor errors more often assign high suspiciousness to benign code than low suspiciousness to backdoored code, while score distributions vary little across attackers.The histograms are bimodal for all but the weakest monitors.Source: §C.4 · p. 22

C.5 ATTACKER PROMPT VARIATIONS

  • Four prompting strategies, from base prompts to monitor names and examples, produced no significant monitoring shift or attacker-strength variation.The later strategies told attackers they would be monitored, disclosed the monitor’s name, and showed examples of caught and missed backdoors.Source: §C.5 · p. 22, Figure 11 · p. 23

C.6 MONITOR PROMPT ABLATIONS

  • The 1–100 scoring scale showed no significant difference from 1–10, although monitors rarely used values not divisible by five on the finer scale.The authors note that finer distinctions may help at the right tail when auditing budgets are low, and leave ways to improve score resolution for future work.Source: §C.6 · p. 24, Figure 12 · p. 24

C.7 FIXING MONITOR MISCALIBRATION

  • Combining suspiciousness and correctness scores improves calibration, but doubles inference costs; the compound score never loses more than 1% of suspiciousness-score AUC and sometimes gains a few points.The authors therefore did not use this strategy in the main paper.Source: §C.7 · p. 24

C.8 ADDITIONAL SAFETY VS AUDITING PLOTS

  • Batch safety can fall below sequential safety in some cases, and the authors conjecture this is related to ROC convexity.They explain that sequential time-dependent thresholds are not contained in the batch setting’s single-threshold action space, so hard thresholding is not always the right batch strategy.Source: §C.9 · p. 25, §C.8 · p. 25

C.9 NON-CONVEX ROC CURVES

  • For a non-convex ROC, convexifying the classifier makes batch safety dominate sequential safety at small auditing budgets; sequential safety remains nearly unchanged.The authors conclude that strategies for a monitor with a non-convex ROC should be probabilistic, with randomness used to construct classifiers on the convex hull.Source: §C.9 · pp. 25, 27, Figure 15 · p. 27

D.2 EXAMPLE #2: SONNET 3.7 COT, INTRODUCTORY DIFFICULTY

The examples show how attackers can produce code that passes public tests while retaining subtle flaws exposed by uncovered cases.

D.2 EXAMPLE #2: SONNET 3.7 COT, INTRODUCTORY DIFFICULTY

  • Backdoors satisfy every public test but fail on at least one uncovered input, making honest mistakes and intentional flaws ambiguous without correctly sourced solutions.The pipeline uses correct APPS solutions as a reference for separating these categories.Source: §D.2 · p. 29
  • Sonnet 3.7 CoT changes inequality strictness, a flaw possible when public tests omit the corresponding boundary case.The example contrasts this backdoored solution with the APPS solution, which mostly handles corner cases.Source: §D.2 · p. 29

D.3 EXAMPLE #3: O3-MINI, COMPETITION DIFFICULTY

  • o3-mini introduces a natural-looking off-by-one error, but it succeeds only if public tests happen not to expose it.The code substitutes used[u:v-1] for used[t1:t2].Source: §D.3 · p. 30

E CHARACTERISTICS OF OPTIMAL BLUE TEAM AUDITING

The section characterizes optimal auditing thresholds and finite-horizon schedules, then examines attacker responses under exponential auditing strategies.

E CHARACTERISTICS OF OPTIMAL BLUE TEAM AUDITING

  • The suspiciousness threshold s is non-decreasing in backdoor probability pb and non-increasing in auditing budget c.This characterizes how the threshold changes with attacker incidence and available auditing resources.Source: E CHARACTERISTICS OF OPTIMAL BLUE TEAM… · p. 31
  • For finite auditing, swapping a larger later budget with a smaller earlier one cannot improve red-team winning probability, so an optimal schedule can be non-increasing.The lemma’s swap argument applies to finite horizons only; its adjacent-swap decomposition does not extend to the infinite case.Source: E CHARACTERISTICS OF OPTIMAL BLUE TEAM… · pp. 32–33

F OPTIMAL RED TEAM RESPONSES IN SEQUENTIAL TRUSTED MONITORING

  • Under exponential auditing strategies with total budget 0.05, red-team win probability can have maxima near λ/N and at pb = 1.Which maximum is more prominent depends on whether the strategy allocates more auditing early or distributes it more evenly; setting p(0) = 1 avoids the pb = 1 maximum.Source: F OPTIMAL RED TEAM RESPONSES IN… · pp. 33–34

G SEQUENTIAL ANYTIME TRUSTED MONITORING

The paper extends trusted monitoring to an unknown, extendable horizon, analyzes attacker responses numerically, and supplies finite-horizon derivations for comparison.

G SEQUENTIAL ANYTIME TRUSTED MONITORING

  • In the anytime setting, weaker attackers tend toward immediate backdoors, stronger attackers toward pb → 0, and intermediate cases can have an interior optimum.For the stronger-attacker regime, the supremum is approached as pb → 0 even though setting pb = 0 gives red-team win probability zero.Source: Figure 16 · p. 34, G SEQUENTIAL ANYTIME TRUSTED MONITORING · p. 34
  • The anytime setting models an unknown number of monitoring steps with an auditing budget p: N → [0, 1], unlike prior known finite-horizon work.The analysis assumes p is non-increasing, reflecting scrutiny that decreases or resources that become limited over time.Source: G SEQUENTIAL ANYTIME TRUSTED MONITORING · p. 34
  • The optimal attacker behavior in anytime monitoring remains an open problem; its proposed dependence on ROC-curve shape is conjectural.The authors call for deeper investigation of that relationship.Source: G SEQUENTIAL ANYTIME TRUSTED MONITORING · p. 34

H.1 SAFETY OF UPFRONT AUDITING

  • The upfront-auditing asymptotic derivation substitutes pb = λ/N and recovers equation 4 of the main paper..Source: §H.1 · p. 35

H.2 ASYMPTOTICS OF BATCH TRUSTED MONITORING

  • For batch trusted monitoring, the asymptotic optimal backdooring rate satisfies λ* = ˆλ + o(1).The derivation obtains this by uniform convergence near ˆλ.Source: §H.2 · p. 36

H.3 SEQUENTIAL NOT ANYTIME TRUSTED MONITORING WITH UNIFORM ALLOCATION STRATEGY

The appendix establishes an immediate-attack optimum under uniform finite-horizon auditing and formulates an asymptotic online game for nonuniform allocations.

H.3 SEQUENTIAL NOT ANYTIME TRUSTED MONITORING WITH UNIFORM ALLOCATION STRATEGY

  • With a constant auditing allocation over N rounds, the red team’s win probability is maximized at pb = 1.Because per-turn success probability is unchanged, delaying offers no advantage, and the attacker loses if it does not insert a backdoor within N turns.Source: §H.3 · p. 37

H.4 ONLINE NOT ANYTIME TRUSTED MONITORING

  • When pb = λ/N, backdoor incidence converges to a Poisson point process over [0, 1] with rate λ.The blue team’s allocation is represented by a Riemann-integrable function p.Source: §H.4 · pp. 38–39
  • The asymptotic online setting frames the attacker’s rate choice and blue team’s allocation as a minimax optimization problem.The blue team’s strategy is chosen for an optimal outcome in the game equilibrium.Source: §H.4 · pp. 38–39

J NUMERICAL OPTIMIZATION OF THE SNAC PROBLEM

The numerical optimization appendix compares exact and limiting SNAC formulations, while the SHADE-Arena evaluation finds that a small safety gain can carry a large cost premium. Together, these results show how optimization choices and deployment setting affect safety-cost estimates.

J NUMERICAL OPTIMIZATION OF THE SNAC PROBLEM

  • The optimization implements both the exact finite-N problem and its limiting approximation, with outer minimization over a constrained strategy set.The appendix describes separate finite and limiting formulations.Source: J NUMERICAL OPTIMIZATION OF THE SNAC… · pp. 40–41
  • Because optimization can get stuck in local minima, the main-paper figures use 50 parallel runs from varied starting strategies.For appendix figures other than Figure 18, computational constraints lead to a specified fixed starting value for k.Source: J NUMERICAL OPTIMIZATION OF THE SNAC… · p. 40
  • The inner maximization is over a scalar grid, preserving differentiability of the outer minimization with respect to p.The appendix uses discrete candidate sets for pb or λ.Source: J NUMERICAL OPTIMIZATION OF THE SNAC… · p. 40
  • To optimize monitor-performance functions, the method uses Gaussian-kernel density estimates and linear interpolation over 5,000 suspiciousness values.The kernel has σ = 3, and interpolation supports solving for s(pi, pb).Source: J NUMERICAL OPTIMIZATION OF THE SNAC… · p. 41
  • From N = 100, the limit approximation is indistinguishable from the exact expression and is faster to compute and easier to implement.Figure 17 shows limit-approximation expressions around the maximizing p∗.Source: J NUMERICAL OPTIMIZATION OF THE SNAC… · p. 40, Figure 17 · p. 41

K CONTROL TAX ON SHADE-ARENA

  • Safety rose from ∼0.73 with GPT 5 Mini to ∼0.78 with GPT 5 as cost increased from $20 to $120 on SHADE-Arena.The figure describes a small marginal safety improvement at the top of the Pareto frontier with a large cost premium.Source: Figure 18 · p. 42, K CONTROL TAX ON SHADE-ARENA · p. 42
  • The SHADE-Arena evaluation reuses 185 Gemini 2.5 Pro rollouts and scores monitors at auditing budget c = 0.05.The rollouts include 93 with a side task and 92 without; monitors classify benign trajectories versus those containing a side task.Source: K CONTROL TAX ON SHADE-ARENA · p. 42

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