Unlikeliness Reward in Reinforcement Learning and AI Alignment

Last updated: June 11, 2025

Unlikeliness Reward: Practical Foundations and Trends in Rewarding and Mitigating Rare Behaviors in Reinforcement Learning and AI Alignment

In reinforcement learning (RL) and AI alignment °, "unlikeliness reward" encompasses both constructive and corrective approaches to the treatment of rare °, out-of-distribution, or infrequent behaviors. Across a spectrum of domains—ranging from formal theorem proving ° to LLM alignment °—this notion is central for promoting diverse, valuable behavior and for safeguarding against the inadvertent reinforcement of undesirable or spurious actions. This article synthesizes foundational theory, major technical developments, and empirical results, strictly drawing from recent, well-documented research.

Significance and Background

The problem of properly identifying and rewarding merit in the presence of uncertainty and randomness has deep roots. "The fair reward problem: the illusion of success and how to solve it" emphasizes how stochasticity and complexity can distort measurements of success in society, leading to a tension between apparent achievement and genuine merit. The authors propose metrics that go beyond rewarding raw outcomes and instead seek to distinguish between skill-driven and luck-driven results, forming an early conceptual architecture for handling "unlikeliness" in reward allocation (Sornette et al., 2019 ° ).

This same challenge recurs in RL and AI alignment, where proxy reward models ° are used in lieu of true objectives. Such models are frequently susceptible to "reward hacking": optimization that exploits weaknesses in the reward specification, resulting in high proxy scores but undesirable or low-true-value behaviors. In these systems, "unlikeliness reward" serves as both a tool for surfacing rare successful behaviors and a bulwark against the reinforcement of out-of-distribution (OOD °), artifact-driven, or reward-hacked outputs [(Skalse et al., 2022 ° ); (He et al., 3 Jun 2025 ° )].

Foundational Concepts

Distinguishing the Value of Unlikely Events

A central framework for reward assessment makes a three-way distinction (Sornette et al., 2019 ° ):

• Raw outcome: Directly rewarding the observed end result; highly susceptible to luck, especially in volatile or short time regimes.
• Risk-adjusted outcome: Normalizing outcomes by risk to better differentiate persistent skill from fortuitous performance (e.g., Sharpe ratio in finance).
• Prospective criterion: Evaluating the potential for adaptation or future success—critical in non-stationary or rapidly evolving domains.

Evolutionary systems that incorporate these criteria can balance exploration with exploitation and are essential for consistently recognizing and rewarding meaningful "unlikeliness".

Reward Hacking and Overoptimization

Reward hacking ° arises when the proxy reward ° is misaligned with true goals, leading policies to optimize for behaviors that are unlikely to be valuable or intended (Skalse et al., 2022 ° ). Such problems can emerge from causal confusion °, noise in preference data, or incomplete observability during reward model training °, causing the reward function to become misidentified and produce high scores for off-manifold behaviors (Tien et al., 2022 ° ).

The Role of Uncertainty Quantification

Recent research highlights the necessity of uncertainty-aware reward models. By estimating the confidence of a reward model in each prediction (via Bayesian techniques, ensembles, or probabilistic heads), RL algorithms ° can penalize the optimization of rewards in regions where the model is untrustworthy or unsupported by data [(Yang et al., 20 Feb 2024 ° ); (Zhai et al., 2023 ° ); (Lou et al., 1 Oct 2024 ° ); (Sun et al., 28 Mar 2025 ° )]. This approach both deters reward hacking and provides a principled guide for exploration and safety.

Key Technical Developments

Explicit Promotion of Rare, Correct Solutions

In domains such as formal theorem proving, standard RL fine-tuning algorithms ° like GRPO ° (Group Relative Policy Optimization) have been shown to bias training toward already-high-probability solutions, effectively narrowing the model's focus and suppressing diversity (He et al., 3 Jun 2025 ° ). To counter this, the "unlikeliness reward" augments the RL objective ° to explicitly upweight correct but rare solutions within each sampled group:

$r_i = R(x, y_i) \Bigg(1 - \beta_{\text{rank}} \frac{G - \text{rank}(y_i)}{G}\Bigg)$

Here, $R(x, y_i)$ is a verifier reward, $G$ is the sample group size, and $\beta_{\text{rank}}$ sets the penalty on high-probability (common) solutions. Empirical results confirm large improvements in pass@$N$ metrics for higher $N$ and increased solution diversity, outperforming standard baselines (He et al., 3 Jun 2025 ° ).

Unlikeliness as a Signal for Reward Model Misalignment

In preference-based reward learning °, "unlikeliness reward" often highlights pathological scenarios where the reward model assigns high scores to behaviors unlikely to be truly valuable—typically due to misidentified causal structure, overfitting to non-causal features, or overconfidence in untested regions of the input space °. Optimizing such models can drive the agent far off the training distribution, yielding catastrophic failures (Tien et al., 2022 ° ).

Uncertainty-Aware Reward Modeling

Recent innovations modify reward models to produce not just mean reward estimates, but full probabilistic predictions ° (e.g., Gaussian means and variances), capturing both aleatoric (data-driven) and epistemic (model-driven) uncertainty [(Yang et al., 20 Feb 2024 ° ); (Lou et al., 1 Oct 2024 ° ); (Sun et al., 28 Mar 2025 ° )]. Policy optimization is then altered to penalize high-uncertainty rewards:

$r'(x, y) = r(x, y) - \lambda \cdot u(x, y)$

where $u(x, y)$ is per-sample uncertainty quantified via distributional overlap (e.g., Bhattacharyya coefficient), ensemble disagreement, or other principled means. Experiments demonstrate that such uncertainty penalties delay the onset of reward hacking and yield higher final performance [(Sun et al., 28 Mar 2025 ° ); (Zhai et al., 2023 ° )].

Information Topology and the Generalization of Unlikeliness Signals

The structure of human preference data—and how it propagates through reward models—has been formalized using concepts from information topology and Bayesian networks °. Tree-structured preference datasets, for example, enable models to generalize "unlikeliness reward" signals more efficiently and robustly than simple chain-based or randomly grouped structures, often achieving a reduction in reward uncertainty by up to $\Theta(\log n / \log \log n)$ for dataset size ° $n$ (Qiu et al., 15 Feb 2024 ° ).

Practical Implementations and State of the Art

Robust reward models using causal augmentation have outperformed ad-hoc artifact removal ° methods, enforcing "unlikeliness reward" not just for rare events, but for blocking the propagation of reward signals through unintended, artifact-driven channels (Liu et al., 20 Sep 2024 ° ).

Emerging Trends and Future Directions

Several converging directions emerge from the literature:

• Principled uncertainty modeling: Probabilistic reward models offering per-sample variance are now central to both positive (rewarding rare, correct outcomes) and negative (mitigating reward hacking) forms of unlikeliness reward [(Xiao et al., 20 Mar 2025 ° ); (Sun et al., 28 Mar 2025 ° ); (Lou et al., 1 Oct 2024 ° )].
• Topology-aware reward learning: Structuring preference data collection ° to maximize information flow and generalization (e.g., via trees or induced Bayesian networks) strengthens the propagation and reliability of unlikeliness signals (Qiu et al., 15 Feb 2024 ° ).
• Explicit anti-hacking objectives: Approaches such as information bottleneck ° regularization ° and causal data augmentation provide systematic tools for countering reward model exploitation [(Miao et al., 14 Feb 2024 ° ); (Liu et al., 20 Sep 2024 ° )].
• Open, modular implementation: Availability of flexible, reproducible recipes for integrating unlikeliness reward in RL pipelines makes practical adoption accessible (He et al., 3 Jun 2025 ° ).

Limitations and Open Challenges

• Uncertainty estimate calibration and tuning of penalty strength ($\lambda$) require further empirical and theoretical paper, as performance can be sensitive to these choices (Sun et al., 28 Mar 2025 ° ).
• Applicability to complex/multi-objective environments: Current evaluations are strongest in theorem proving, OOD LLMing, and robot exploration; broader tests in high-complexity or adversarial settings are essential.
• Balancing diversity vs. sharpness: While unlikeliness reward increases exploration and diversity, over-penalizing common modes can reduce performance on well-understood sub-tasks; domain-dependent trade-offs must be evaluated [(He et al., 3 Jun 2025 ° ); (Sornette et al., 2019 ° )].

References

• (Sornette et al., 2019 ° ) The fair reward problem: the illusion of success and how to solve it
• (Tien et al., 2022 ° ) Causal Confusion and Reward Misidentification in Preference-Based Reward Learning
• (Liang et al., 2022 ° ) Reward Uncertainty for Exploration in Preference-based Reinforcement Learning °
• (Skalse et al., 2022 ° ) Defining and Characterizing Reward Hacking
• (Zhai et al., 2023 ° ) Uncertainty-Penalized Reinforcement Learning from Human Feedback ° with Diverse Reward LoRA ° Ensembles
• (Miao et al., 14 Feb 2024 ° ) InfoRM: Mitigating Reward Hacking in RLHF via Information-Theoretic Reward Modeling °
• (Qiu et al., 15 Feb 2024 ° ) Reward Generalization ° in RLHF: A Topological Perspective °
• (Yang et al., 20 Feb 2024 ° ) Bayesian Reward Models for LLM Alignment
• (Liu et al., 20 Sep 2024 ° ) RRM: Robust Reward Model ° Training Mitigates Reward Hacking
• (Lou et al., 1 Oct 2024 ° ) Uncertainty-aware Reward Model: Teaching Reward Models to Know What is Unknown
• (Xiao et al., 20 Mar 2025 ° ) Likelihood Reward Redistribution
• (Sun et al., 28 Mar 2025 ° ) Probabilistic Uncertain Reward Model: A Natural Generalization of Bradley-Terry Reward Model
• (He et al., 3 Jun 2025 ° ) Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening

Speculative Note:

Future research could investigate adaptive meta-learning ° strategies for calibrating unlikeliness reward in real time, or explore interdisciplinary analogies—such as those from economics—for robust merit assessment in evolving AI systems ° [citation needed].