Temper and Tilt Lead to SLOP: Reward Hacking Mitigation with Inference-Time Alignment

Inference-time alignment steers a frozen language model during decoding using auxiliary reward signals, avoiding the cost of repeated weight updates. However, existing inference-time alignment methods typically optimize a single scalar score, so explicit safety constraints must either be ignored or encoded through manually tuned penalties. We propose Lagrangian Reward Augmentation (LARA), a general inference-time alignment framework under safety constraints. Starting from a KL-regularized constrained objective with a reward model and a cost model, LARA dualizes the constraint and reduces the optimization problem to a one-dimensional convex problem over a nonnegative dual variable. Estimated on a small calibration set, this dual variable defines an augmented reward that can be used as a drop-in scoring signal within existing inference-time alignment methods. For sequence-level sampling methods, such as Best-of-N reranking, the calibrated dual variable corresponds to the solution of the expected-cost constrained problem. For token-level reward-guided decoding methods, the same construction yields a principled dual-calibrated heuristic rather than an exact constrained-policy guarantee. We evaluate LARA on both sequence-level and token-level inference-time alignment methods, and find that LARA improves the helpfulness-harmlessness tradeoff, with Best-of-N achieving the best performance among inference-time methods, approaching finetuning-based direct alignment baselines.

Ensuring the reliability of Large Language Models (LLMs) under distribution drift requires inference-time adaptation. While inference-time alignment methods such as Best-of-$N$ and rejection sampling are widely used, they frame the task as a sampling-intensive, reward-guided search, leading to two key limitations: their performance is bounded by the base model's generation quality, and their reliance on imperfect reward models makes them vulnerable to reward hacking. To address these challenges, we introduce Gradient-Guided Reward Optimization (GGRO), a lightweight inference-time method that performs targeted, minimal intervention during decoding via gradient guidance. Specifically, GGRO monitors token-level entropy to identify high-uncertainty regions indicative of drift or misalignment. Upon detection, it responds by injecting nudging tokens, generated using gradient signals from an off-the-shelf reward model, to steer the generation trajectory rather than merely re-ranking samples. Experiments show that GGRO consistently improves inference-time alignment across safety, helpfulness, and reasoning benchmarks. It also increases coverage of high-quality responses and robustness to reward hacking, with minimal computational overhead. Code is available at https://github.com/lhk2004/GGRO.

Preference-based fine-tuning methods such as RLHF and DPO require substantial compute and large preference datasets. They also need direct access to the model parameters which are not provided by many state-of-the art models. Inference-time alignment offers a cost-effective alternative without updating model parameters. However, existing inference-time methods rely on a scalar reward model derived under a Bradley-Terry assumption, which cannot represent general preferences. Following recent work on fine-tuning with generalized preferences, in this work, we initiate the study of inference-time alignment under general preferences. We formulate the problem as obtaining a Nash equilibrium of a two-player zero-sum game between policies. We propose two algorithms: Best-of-Nash (BoN) and Nash Mirror Descent (NMD). We prove that both algorithms achieve a duality gap that matches the problem lower bound. Empirically, we implement the two methods on three datasets, which shows that our methods substantially outperform the base policy, converging to the performance of the fine-tuned models. Moreover, our results show that NMD remains robust across the regularization parameter.