This work shows that $\beta$ entangles two distinct roles: it governs the effective inverse preference-noise scale and simultaneously rescales the optimization dynamics, coupling this scale with the effective step size, and proposes a centered-softplus reformulation that is argmin-equivalent to DPO for $\beta>0$, while making the inverse preference-noise-scale and learning-rate effects explicit and independently tunable.
Abstract
Direct Preference Optimization (DPO) is a widely used objective for aligning language models from preference data, with the coefficient $\beta$ commonly interpreted as controlling the KL constraint to a reference policy. We show that $\beta$ entangles two distinct roles: it governs the effective inverse preference-noise scale and simultaneously rescales the optimization dynamics, coupling this scale with the effective step size. As a consequence, at a fixed learning rate the achieved policy deviation is non-monotone in $\beta$: it vanishes in a dead zone at small $\beta$, reaches a peak at an intermediate value, and decreases again for larger $\beta$. Moreover, standard DPO loss values are not comparable across $\beta$: runs with nearly identical loss curves can differ several-fold in KL divergence from the reference model. This entanglement obscures the role of $\beta$, increases sensitivity to hyperparameter choices, and complicates learning-rate scheduling. We propose a centered-softplus reformulation that is argmin-equivalent to DPO for $\beta>0$, while making the inverse preference-noise-scale and learning-rate effects explicit and independently tunable. The normalized centered-softplus objective also admits a continuous $\beta\to0$ endpoint that reduces to a linear preference-margin objective.
On-policy self-distillation (OPSD) is a promising approach to improve reasoning language models, but it remains brittle in practice: making it work reliably often requires substantial engineering effort. We identify a structural source of this difficulty: vanilla OPSD is precisely the $\beta=1$ member of a broader policy-optimization family, where $\beta$ weights the KL penalty anchoring the student to a reference policy. This equivalence turns $\beta$ from an implicit value fixed at one into a controllable regularization parameter, yielding a more general formulation that trades off proximity to a reference policy against privileged teacher guidance. We introduce $\beta$-OPSD and derive its optimal policy as a geometric interpolation between the reference policy and the privileged teacher. Directly optimizing this objective with reinforcement learning, however, would be costly and high-variance. Rather than optimize the RL objective directly, we turn its closed-form solution into a distillation target. Each value of $\beta$ selects a target along the reference-to-teacher path, which we implement efficiently by mixing their token-level logits. In this way, inexpensive distillation approximates the solution of expensive policy optimization. Return-to-go credit assignment further aligns token updates with the sequence-level objective while retaining the simplicity of OPSD. Experiments on mathematical reasoning benchmarks show that $\beta$-OPSD consistently outperforms vanilla OPSD, improving optimization stability and downstream reasoning performance. Our results provide a principled route from self-distillation to policy optimization and back without sacrificing the efficiency that makes OPSD practical.
Jiawei Xu, Minghui Liu, Juzheng Zhang et al.· 1 citation
Environment-Regularized Policy Optimization (ERPO) replaces the standard Policy-KL regularizer while achieving effective control over query distribution drift, delivering stronger accuracy and substantially more stable behavior under high-temperature decoding and long-horizon training.
Xianlei Zhou, Xiangdi Meng, Yu He et al.· 0 citations
This work proposes VPO, a negative gradient constraint method for human non-preference samples based on V -usable information, which can alleviate the squeezing effect of DPO, enhance alignment with the generation objective, and maintain the model’s ability to distinguish between preference and non-preference samples.
Zecheng Wang, Chunshan Li, Yupeng Zhang et al.· Neural Information Processin...· 1 citation
Using Evolutionary Strategies (ES) for fine-tuning large language models is attractive because it is memory-efficient, parallel, and compatible with black-box or discrete rewards. Yet its population-size conclusions conflict sharply: fine-tuning with cross-entropy (CE) reward succeeds with $N=1$, while binary-reward training often needs $N \approx 30$. We show this gap is largely about reward design and normalization, not population size. In the capable-model regime we study, z-score advantage normalization can cause $N=2$ to fail. Disabling normalization lets binary-reward ES with $N=2$ improve on GSM8K and TREC across capable models spanning 0.5B-7B, where the normalized variant collapses or degrades. This small-$N$ risk is set by reward granularity: binary accuracy reward induces a zero-advantage probability $q$ that depends in closed form on base accuracy, batch size, and intra-pair correctness correlation; a zero-training probe on Qwen2.5-Instruct/GSM8K matches the formula with mean absolute error 0.020 across 12 configurations and finds the availability threshold $N_{\mathrm{avail}}$ to be small in this capable-model regime. The implication is not that $N=2$ is universally sufficient, but that small-population failure in capable-model binary ES can be an implementation artifact rather than an intrinsic population limit.
In a $\beta$-VAE, increasing the regularization strength acts as a spectral cutoff by collapsing low-utility latent coordinates. In the linear Gaussian VAE, the collapse order matches the ranking of reconstruction utilities exactly, because both are set by the PCA spectrum. We ask which parts of this picture survive in fully connected nonlinear VAEs trained on WorldClim. We find that nonlinear interactions shift and broaden collapse onsets, so thresholds no longer coincide exactly with utilities. However, the common ordering is preserved over the resolved ranks, so the spectral cutoff still acts as a utility cutoff and the effective-description logic carries through. The resulting effective-dimension curves reveal a head--tail tradeoff: increasing depth concentrates utility into the first few coordinates but worsens tail fidelity.
Multi-preference alignment is often framed as scalarization: combine reward dimensions, then optimize. This leaves a temporal decision underspecified: when should each preference dimension enter policy optimization? We propose \methodname, a stability-guided active-set controller for controlled objective admission. \methodname starts from a small active set, retains admitted objectives, and expands when reward-deviation gates indicate low recent deviation or a patience budget is exhausted. A probing phase estimates a hard-to-easy order, and adaptive weighting emphasizes underperforming active dimensions. Automatic evaluations with 15 training preferences and 16 held-out benchmark columns show that \methodname obtains higher averages than simultaneous scalarization and shared-budget adapted baselines. Component ablations and expansion dynamics further support cumulative retention, gated admission, and probing-derived ordering as useful design choices in this setting. These results position objective-entry timing as a concrete control variable in reward-vector RLHF.
Yongqi Tong, Z. Zhang, Ruirui Wang et al.· 0 citations