We prove that under five minimal axioms -- multi-dimensional quality, finite evaluation, effective optimization, resource finiteness, and combinatorial interaction -- any optimized AI agent will systematically under-invest effort in quality dimensions not covered by its evaluation system. This result establishes reward hacking as a structural equilibrium, not a correctable bug, and holds regardless of the specific alignment method (RLHF, DPO, Constitutional AI, or others) or evaluation architecture employed. Our framework instantiates the multi-task principal-agent model of Holmstrom and Milgrom (1991) in the AI alignment setting, but exploits a structural feature unique to AI systems -- the known, differentiable architecture of reward models -- to derive a computable distortion index that predicts both the direction and severity of hacking on each quality dimension prior to deployment. We further prove that the transition from closed reasoning to agentic systems causes evaluation coverage to decline toward zero as tool count grows -- because quality dimensions expand combinatorially while evaluation costs grow at most linearly per tool -- so that hacking severity increases structurally and without bound. Our results unify the explanation of sycophancy, length gaming, and specification gaming under a single theoretical structure and yield an actionable vulnerability assessment procedure. We further conjecture -- with partial formal analysis -- the existence of a capability threshold beyond which agents transition from gaming within the evaluation system (Goodhart regime) to actively degrading the evaluation system itself (Campbell regime), providing the first economic formalization of Bostrom's (2014) "treacherous turn."
Figures & tables
Propositions 1–2
Conjectures 1–2
Axiom base
Axioms 1–5: undeniable
Assumption C1: plausible but not undeniable
Agent behavior
Takes evaluation as given
May actively degrade evaluation
Proof status
Complete
Partial (monotonicity condition unverified in general)
Reward hacking studies how AI systems exploit imperfect objectives and how to detect, measure, and prevent behavior that scores well but misses intent.
Aligning autonomous agents with human intent remains a central challenge in modern AI. A key manifestation of this challenge is reward hacking, whereby agents appear successful under the evaluation signal while violating the intended objective. Reward hacking has been observed across a wide range of settings, yet methods for reliably measuring it at scale remain lacking. In this work, we introduce a new evaluation paradigm for measuring reward hacking. Whereas prior studies have primarily analyzed it post hoc by inspecting agent trajectories, we instead embed detectable reward hacking opportunities directly into environments. This makes their exploitation verifiable by design, enabling deterministic and automated measurement of whether and how agents exploit such vulnerabilities. We instantiate this approach in TextArena and release Hack-Verifiable TextArena, a testbed in which reward hacking can be measured reliably. Using this benchmark, we analyze reward hacking behavior across language models in diverse environments and settings. We open source the code at https://github.com/MajoRoth/hack-verifiable-environments/.
Amit Roth, Ankur Samanta, Matan Halevy +2
1Tel Aviv University · 2Columbia University · 3Taso Labs
Reward hacking, where AI systems exploit misspecified objectives to achieve high reward without satisfying intended goals, remains a central challenge in AI safety. Yet most known instances have been discovered post hoc in frontier systems where controlled study is impractical. We adapt the AI Safety Gridworlds framework into a text-based evaluation suite that reformulates classic reinforcement learning safety tasks for language-based agents. Across frontier and mid-scale models, we find that specification gaming emerges zero-shot: models systematically achieve high observed reward while underperforming on hidden safety objectives, and even apparently safe behaviors can reflect misunderstanding rather than principled safety. Reinforcement learning does not correct these failures: direct reward optimization widens the gap between observed and hidden reward, as the model's initial competence causes it to lock into locally rewarding strategies before discovering safer alternatives. This pattern persists across model scales (1.5B--14B) and is not resolved by finer credit assignment, exploration prompts, or entropy regularization. Our results show that reward hacking arises naturally when optimizing proxy objectives with capable language model agents and resists standard mitigations, suggesting that proxy-reward failures in agentic settings may require approaches beyond standard exploration and credit-assignment fixes. To facilitate reproducibility, the code for this work is available at our public repository.
Ömer Veysel Çağatan, Xuandong Zhao
KUIS AI Center, Koc¸ University · Istanbul, Türkiye · University of California, Berkeley +1
Agent benchmarks have become the de facto measure of frontier AI competence, guiding model selection, investment, and deployment. However, reward hacking, where agents maximize a score without performing the intended task, emerges spontaneously in frontier models without overfitting. We argue that benchmarks must be secure by design. From past incidents of reward hacks, we derive a taxonomy of eight recurring flaw patterns and compile them into the Agent-Eval Checklist for benchmark designers. We condense the insights into BenchJack, an automated red-teaming system that drives coding agents to audit benchmarks and identify possible reward-hacking exploits in a clairvoyant manner. Moreover, we extend BenchJack to an iterative generative-adversarial pipeline that discovers new flaws and patches them iteratively to improve benchmark robustness. We apply BenchJack to 10 popular agent benchmarks spanning software engineering, web navigation, desktop computing, and terminal operations. BenchJack synthesizes reward-hacking exploits that achieve near-perfect scores on most of the benchmarks without solving a single task, surfacing 219 distinct flaws across the eight classes. Moreover, BenchJack's extended pipeline reduces the hackable-task ratio from near 100% to under 10% on four benchmarks without fatal design flaws, fully patching WebArena and OSWorld within three iterations. Our results show that evaluation pipelines have not internalized an adversarial mindset, and that proactive auditing could help close the security gap for the fast-paced benchmarking space.