Preference-Based Proximal Policy Optimization

• Preference-based Proximal Policy Optimization is an RL framework that integrates human and task-based feedback to guide dynamic policy updates.
• It replaces traditional reward signals with comparative feedback, using reward modeling and adaptive clipping to enhance policy performance.
• The method has demonstrated improved alignment, sample efficiency, and stability across simulated and real-world robotic applications.

Preference-based Proximal Policy Optimization (Pb-PPO) encompasses a family of reinforcement learning (RL) algorithms that optimize policies based on preference signals, either from humans or task-based returns, rather than solely through explicit reward functions. Pb-PPO variants quantify and leverage implicit preferences—such as comparative feedback or return maximization—to address challenges in environments where reward specification is impractical or preference alignment is critical. These methods build upon and extend Proximal Policy Optimization (PPO), dynamically incorporating preference information into policy updates, reward modeling, or hyperparameter adaptation.

1. Foundations and Motivation

Traditional PPO is widely used for RL due to its stability, relying on a surrogate objective with policy ratio clipping to constrain updates. However, standard PPO presupposes access to dense, well-shaped reward signals and requires hand-tuning of key hyperparameters (e.g., the clipping threshold $\epsilon$). Several settings challenge this paradigm:

• Preference-based RL: Many tasks, especially in LLM alignment and robotics, require agents to learn from relative judgments rather than absolute rewards. Human feedback often arrives in the form of comparative labels or rankings (e.g., "Trajectory A is preferred over Trajectory B").
• Complex or Implicit Objectives: In domains such as acrobatic flight, reward engineering is both labor-intensive and prone to misalignment with true task goals or human intent.
• Hyperparameter Sensitivity: The choice of PPO’s clipping bound materially affects learning dynamics, but no single fixed value is optimal throughout training.

Preference-based PPO frameworks address these issues via three main approaches:

1. Replacing reward-based policy updates with preference-driven (relative/comparative) objectives.
2. Employing preference-based reward modeling, sometimes leveraging probabilistic or ensemble uncertainty.
3. Dynamically controlling the PPO update mechanism (notably, the clipping bound) using task-level or human-derived preference signals.

2. Pairwise Proximal Policy Optimization (P3O) and Preference Supervision

The "Pairwise Proximal Policy Optimization" (P3O) algorithm (Wu et al., 2023) is designed for RL scenarios where supervision naturally takes the form of pairwise preferences over trajectories, typical in RLHF for LLMs. P3O directly optimizes the policy using trajectory-level reward differences, bypassing the need for per-token advantage estimation and manual reward calibration.

• Key Objective: The policy gradient is computed using the difference in reward between two trajectories for the same context:

$$\nabla \mathcal{L}^{\text{P}3\text{O}} = \mathbb{E}_{a_1,a_2 \sim \pi_{\theta_\text{old}}(\cdot|x)}\Bigg[ (r(a_1|x) - r(a_2|x)) \frac{\pi_{\theta}(a_1|x)}{\pi_{\theta_\text{old}}(a_1|x)} \frac{\pi_{\theta}(a_2|x)}{\pi_{\theta_\text{old}}(a_2|x)} \cdot \frac{1}{2} \nabla \log \frac{\pi_{\theta}(a_1|x)}{\pi_{\theta}(a_2|x)} \Bigg]$$

• Theoretical Properties:
  • Invariance to Additive Reward Shifts: P3O's update depends only on reward differences, making it robust to any additive constant in the reward model for each context.
  • Algorithmic Simplicity: No value function or advantage estimation is needed; the update structure directly mirrors the comparative nature of human feedback.
  • Clipped Variants: Clipping mechanisms, analogous to PPO’s clipped surrogate, are incorporated for stability.
• Empirical Insights:
  • KL-Reward Frontier: P3O achieves superior reward for a given KL divergence with respect to the reference (SFT) policy compared to PPO and DPO.
  • Alignment: P3O-aligned LLMs attain higher win rates in human or GPT-4-based preference evaluations at lower KL, mitigating both overoptimization and reward hacking.
  • Qualitative Behaviors: Output completions are more responsive and instruction-following than PPO or SFT alone.
• Significance: P3O establishes a trajectory-wise policy optimization protocol aligned with the statistical and practical structure of comparative data, removing key sources of algorithmic and reward normalization complexity.

3. Preference-based PPO with Uncertainty and Reward Ensembles

Recent work applies Preference PPO to continuous control and robotics, exemplified by (Merk et al., 26 Aug 2025), which leverages comparative feedback for acrobatic drone flight control.

• Reward Modeling: Preferences over trajectory pairs are used to train a reward model via the Bradley-Terry likelihood, estimating the probability that one trajectory is preferred over another:

$$\hat{p}(\tau_1 > \tau_2) = \frac{\exp(\hat{r}_1)}{\exp(\hat{r}_1) + \exp(\hat{r}_2)}$$

• REC Enhancement: "Reward Ensemble under Confidence" (REC) extends this framework by
  • Modeling reward predictions as Gaussian distributions, enabling the computation of probabilistic preference losses via the standard normal CDF:

  $$p(\tau_1 > \tau_2) = \Phi\left( \frac{r_{\text{mean}}(\tau_1) - r_{\text{mean}}(\tau_2)}{\sqrt{r_{\text{std}}(\tau_1)^2 + r_{\text{std}}(\tau_2)^2}} \right)$$ - Training an ensemble of reward models, aggregating their predictions with additive noise for exploration. - Selecting trajectory pairs for human labeling using ensemble disagreement, directing feedback acquisition to ambiguous regions. - Periodically resetting low-performing ensemble members to maintain diversity.

• Results in Robotics and Simulation:

  • With standard Preference PPO, learned policies achieved $55.2\%$ of the shaped reward baseline for the powerloop task; REC extended this to $88.4\%$.
  • Human reward alignment is weak with hand-designed rewards (only $60.7\%$ agreement), indicating that preference-based models more faithfully capture nuanced task objectives.
  • Policies trained with REC Preference PPO in simulation transfer successfully to real quadrotor platforms without fine-tuning.
• Contextual Importance: These results underscore the value of probabilistic and ensemble-based preference reward modeling for tasks characterized by subjective assessment criteria, multi-modality, and complex physical dynamics.

4. Adaptive PPO via Task Preference: Pb-PPO and Dynamic Clipping

The algorithm Pb-PPO, as specified in (Zhang et al., 2023), dynamically selects the PPO clipping bound $\epsilon$ in response to observed task returns, formalizing the PPO update as a bi-level optimization:

• Bi-level Optimization:
  • Outer Loop (Clipping Bound Selection): A set of candidate clipping bounds $\zeta$ is maintained, each treated as an arm in a multi-armed bandit.
  • Arm Selection: For each PPO update, the arm (i.e., the clipping bound $\epsilon^*$) maximizing the upper confidence bound (UCB) of recent returns is chosen:

  $$\epsilon^* = \arg\max_{\epsilon_i \in \zeta} \left[ U(\epsilon_i) + \lambda \cdot \hat U(\epsilon_i) \right]$$

  where $U(\epsilon_i)$ is the expected return and $\hat U(\epsilon_i)$ quantifies exploration uncertainty. - Inner Loop (Policy Update): The PPO surrogate objective is optimized using the selected $\epsilon^*$:

  $$\mathcal{J}_{\text{PPO-clip}}(\pi_{\text{old}}, \pi_{\text{new}}, \epsilon^*) = \mathbb{E}_{\tau \sim \pi_{\text{old}}} \left[ \min \left( \frac{\pi_{\text{new}}(\tau)}{\pi_{\text{old}}(\tau)} A^{\pi_{\text{old}}}(s_t, a_t), \text{clip}\left(\frac{\pi_{\text{new}}(\tau)}{\pi_{\text{old}}(\tau)}, 1-\epsilon^*, 1+\epsilon^*\right) A^{\pi_{\text{old}}}(s_t, a_t) \right) \right]$$

• Empirical Impact:

  • Pb-PPO outperforms PPO with fixed or other dynamic clipping schemes in Mujoco and PyBullet Gym benchmarks.
  • Improved final returns and sample efficiency are accompanied by enhanced monotonicity and stability of policy updates.
  • The proportion of successful policy improvements (new policy outperforming the old) with Pb-PPO is observed at $5.0\%$, exceeding that of fixed-clipping PPO.
  • The method accommodates both task returns and human-derived feedback as the bandit signal for preference alignment.
• Significance: Pb-PPO embodies a general principle of aligning hyperparameter adaptation (here, the PPO clipping bound) directly with maximization of task- or human-preferred outcomes, contributing to greater learning robustness and performance.

5. Comparative Table of Pb-PPO Approaches and Core Characteristics

Algorithm	Preference Source	Policy Update Granularity	Key Mechanism
P3O (Wu et al., 2023)	Pairwise trajectory feedback	Trajectory-wise	Policy gradient from reward differences
Preference PPO (Merk et al., 26 Aug 2025)	Trajectory rankings/pairs	Trajectory-wise	PPO on learned preference reward
REC Preference PPO	Ensembled, probabilistic reward	Trajectory-wise	Uncertainty-driven feedback and reward model
Pb-PPO (Zhang et al., 2023)	Task/human return	Token/trajectory	Bandit-based dynamic PPO clipping bound

This table summarizes the origin of preference signals, granularity of policy updates, and the core algorithmic innovation for each method.

6. Limitations, Open Issues, and Outlook

Despite their advances, preference-based PPO frameworks entail several unresolved or context-dependent challenges:

• Optimality Guarantees: While methods like P3O offer invariance properties, there is limited theoretical analysis on global convergence or optimality in high-dimensional, non-stationary preference environments.
• Human Feedback Bottlenecks: The effectiveness of preference-based learning is constrained by annotator throughput, reliability, and the presence of ambiguous or inconsistent preferences.
• Exploration-Exploitation Trade-offs: Algorithms such as REC or Pb-PPO adapt better to uncertainty, but further investigation is required to calibrate exploration signals—especially in the presence of sparse or noisy preference data.
• Transfer and Generalization: While sim-to-real results are promising for robotic systems, the degree to which preference-learned policies generalize to distributionally shifted tasks remains an open research question.

A plausible implication is that preference-based approaches—especially as implemented in Pb-PPO variants—will play an increasingly central role in RL for domains where objective specification is infeasible and aligning to complex, evolving preferences is paramount. Empirical findings consistently indicate improved stability, policy alignment, and task performance when compared to reward-dependent or static-hyperparameter baselines.

7. Summary

Preference-based Proximal Policy Optimization constitutes an extensible and theoretically grounded paradigm for RL in both artificial intelligence and robotics, directly engaging with comparative, human-centered, or task-based supervision. By reformulating policy updates and algorithmic scaffolding to accommodate preference signals at multiple levels—policy gradient, reward modeling, and hyperparameter selection—Pb-PPO methods provide a robust alternative to conventional reward-centric RL, particularly in high-dimensional, subjective, and real-world aligned learning tasks.