Foundation Lab

PPO: Proximal Policy Optimization

PPO is THE algorithm behind RLHF—understanding it explains how preference data becomes model behavior

Concept 40 of 100Scaling & AlignmentPhase 7
#40PPOScaling & Alignment
key equation
LCLIP(θ)=E[min⁡(rtA^t,clip(rt,1−ϵ,1+ϵ)A^t)]L^{CLIP}(\theta) = \mathbb{E}\left[ \min\left( r_t \hat{A}_t, \text{clip}(r_t, 1-\epsilon, 1+\epsilon) \hat{A}_t \right) \right]
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Concept 40 of 100PPOScaling & Alignment / Phase 7: Alignment & RLHF
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Why clipping not KL penalty: PPO was simpler to tune than TRPO and empirically as effective

LCLIP(θ)=E[min⁡(rtA^t,clip(rt,1−ϵ,1+ϵ)A^t)]L^{CLIP}(\theta) = \mathbb{E}\left[ \min\left( r_t \hat{A}_t, \text{clip}(r_t, 1-\epsilon, 1+\epsilon) \hat{A}_t \right) \right]
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Why It Matters for Modern Models

  • PPO is THE algorithm behind RLHF—understanding it explains how preference data becomes model behavior
  • Clipping ratio is a practical trust region: prevents catastrophic forgetting while allowing learning
  • GAE balances bias/variance in advantage estimation—key hyperparameter for stable RLHF training

What Tutorials Skip

What is still poorly explained in textbooks and papers:

  • Why clipping not KL penalty: PPO was simpler to tune than TRPO and empirically as effective
  • The "probability ratio" view: you are reweighting old experience by how much more/less likely actions are now
  • PPO failures in RLHF often trace to advantage estimation issues—reward model noise amplifies errors

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Key Equation
LCLIP(θ)=E[min⁡(rtA^t,clip(rt,1−ϵ,1+ϵ)A^t)]L^{CLIP}(\theta) = \mathbb{E}\left[ \min\left( r_t \hat{A}_t, \text{clip}(r_t, 1-\epsilon, 1+\epsilon) \hat{A}_t \right) \right]

PPO optimizes policies with clipped surrogate objectives:

LCLIP(θ)=Et[min⁡(rt(θ)A^t,clip(rt(θ),1−ϵ,1+ϵ)A^t)]L^{CLIP}(\theta) = \mathbb{E}_t\left[ \min\left( r_t(\theta) \hat{A}_t, \text{clip}(r_t(\theta), 1-\epsilon, 1+\epsilon) \hat{A}_t \right) \right]

where the probability ratio is:

rt(θ)=πθ(at∣st)πθold(at∣st)r_t(\theta) = \frac{\pi_\theta(a_t|s_t)}{\pi_{\theta_{\text{old}}}(a_t|s_t)}

Advantage estimation (GAE):

A^t=∑l=0∞(γλ)lδt+l,δt=rt+γV(st+1)−V(st)\hat{A}_t = \sum_{l=0}^{\infty} (\gamma\lambda)^l \delta_{t+l}, \quad \delta_t = r_t + \gamma V(s_{t+1}) - V(s_t)

The clipping prevents too-large policy updates that destabilize training.

Canonical Papers

Proximal Policy Optimization Algorithms

Schulman et al.2017arXiv
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