24Scaling & Alignment

🎯Direct Preference Optimization: RL-Free Alignment from Human Preferences

Canonical Papers

Direct Preference Optimization: Your Language Model is Secretly a Reward Model

Rafailov et al.2023NeurIPS

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Smaug: Fixing Failure Modes of Preference Optimisation with DPO-Positive

Pal et al.2024arXiv

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SimPO: Simple Preference Optimization with a Reference-Free Reward

Meng et al.2024arXiv

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Core Mathematics

DPO replaces the RLHF reinforcement learning loop with a simple supervised classification loss on preference pairs, while maintaining the same KL-constrained objective.

KL-regularized RLHF objective:

\max_{\pi} \mathbb{E}_{y \sim \pi(\cdot|x)}[r(x,y)] - \beta \cdot \text{KL}(\pi(\cdot|x) \| \pi_{\text{ref}}(\cdot|x))

Closed-form optimal policy (Boltzmann):

\pi^{*}(y|x) = \frac{1}{Z(x)} \pi_{\text{ref}}(y|x) \exp\!\left(\frac{1}{\beta}r(x,y)\right)

DPO loss (RL-free):

Given preference pairs $(x, y_w, y_\ell)$ (winner, loser):

\mathcal{L}_{\text{DPO}}(\theta) = -\mathbb{E}\left[\log \sigma\!\left(\beta \left[\log\frac{\pi_\theta(y_w|x)}{\pi_{\text{ref}}(y_w|x)} - \log\frac{\pi_\theta(y_\ell|x)}{\pi_{\text{ref}}(y_\ell|x)}\right]\right)\right]

This is logistic regression on log-probability ratios—no reward model, no PPO, just supervised learning.

Key Equation

\mathcal{L}_{\text{DPO}} = -\mathbb{E}\left[\log \sigma\!\left(\beta \left[\log\frac{\pi_\theta(y_w|x)}{\pi_{\text{ref}}(y_w|x)} - \log\frac{\pi_\theta(y_\ell|x)}{\pi_{\text{ref}}(y_\ell|x)}\right]\right)\right]

Interactive Visualization

Why It Matters for Modern Models

DPO is how base models become assistants—post-training for helpfulness, harmlessness, instruction-following without full RL loops
Open-model ecosystems (Llama, Mistral, Gemma) use DPO-like recipes because simpler to reproduce than PPO-based RLHF
Frontier is now "loss design, not just DPO"—SimPO removes reference model, DPOP fixes failure modes, showing alignment is optimization engineering
DPO exposes the core mental model: KL-regularized distribution shaping from comparisons, whether you use RL or not
Bridges efficiency arc (#19-23) to alignment—after serving models efficiently, DPO shows how to shape them into useful assistants

Missing Intuition

What is still poorly explained in textbooks and papers:

DPO is "move probability mass," not "learn a scalar reward"—you directly update policy by increasing relative odds of preferred completions
Reference model is behavioral anchor, not detail—KL term is trust-region constraint keeping you on-distribution for feedback signal
Winning the pair ≠ making winner more likely—DPOP shows DPO can increase winner/loser ratio while decreasing absolute likelihood of preferred completion
Offline preference optimization is limited by dataset support—if preference data never contains safety-critical edge cases, DPO won't invent them
DPO turns alignment into logistic regression on log-prob ratios—capturing RLHF's goal without the RL machinery

Connections

Prerequisites

ℒML/CE/KL ⚖RLHF

Enables

👍KTO ⚠️Reward Hacking

Next Moves

Explore this concept from different angles — like a mathematician would.

Semantic Connections

🔧 Invented to Fix

👍No pairs needed→KTO ⚠️Remove reward model→Reward Hacking

⚠️ Breaks When

⚖Reward hacking→RLHF ⚠️Distribution shift→Reward Hacking

🔄 Same Technique

ℒLikelihood ratios→ML/CE/KL

↔️ Mathematical Dual

⚖RL ↔ Classification→RLHF