docs/source_en/Instruction/GRPO/AdvancedResearch/REINFORCEPP.md

REINFORCE++: An Efficient RLHF Algorithm with Robustness to Both Prompt and Reward Models

REINFORCE++ Baseline is a simplified version of the REINFORCE++ algorithm, designed for outcome rewards (response-level scalar rewards). Similar to GRPO, it samples multiple model outputs for each prompt and uses an intra-group baseline to estimate advantages. The key difference lies in the statistics used for normalization.

Algorithm Overview

For clarity, we explain REINFORCE++ Baseline by contrasting it with GRPO (Group Relative Policy Optimization).

Both GRPO and REINFORCE++ Baseline estimate advantages via intra-group comparisons. Their main differences are:

Difference 1: Statistics Used for Normalization

GRPO (Group Relative Policy Optimization)

For each prompt, GRPO generates $G$ response samples and normalizes using the mean and standard deviation of all samples within the group:

$${\widehat{A}}_i=\frac{R_i-\text{mean}(\{R_j{\}}_{j=1}^G)}{\text{std}(\{R_j{\}}_{j=1}^G)}\backslash hat\{A\}\_\{i\}\; =\; \backslash frac\{R\_i\; -\; \backslash text\{mean\}(\backslash \{R\_j\backslash \}\_\{j=1\}^G)\}\{\backslash text\{std\}(\backslash \{R\_j\backslash \}\_\{j=1\}^G)\}$$

When scale_rewards='batch' is set, it uses the batch-level std of original rewards:

$${\widehat{A}}_i=\frac{R_i-\text{mean}(\{R_j{\}}_{j=1}^G)}{\text{std}(\{R_j{\}}_{j=1}^N)}\backslash hat\{A\}\_\{i\}\; =\; \backslash frac\{R\_i\; -\; \backslash text\{mean\}(\backslash \{R\_j\backslash \}\_\{j=1\}^G)\}\{\backslash text\{std\}(\backslash \{R\_j\backslash \}\_\{j=1\}^\{N\})\}$$

where $N$ is the total number of samples in the batch.

REINFORCE++ Baseline

For each prompt, REINFORCE++ generates $G$ response samples, subtracts the group mean, and then normalizes using the standard deviation of the group-mean-subtracted rewards:

where $N$ is the total number of samples in the batch.

Key Difference:

• GRPO: Uses the std of original rewards $R$ for normalization
• REINFORCE++: Uses the std of group-mean-subtracted rewards $\tilde{A}$ for normalization

Difference 2: KL Divergence Regularization

Similar to RLOO, REINFORCE++ Baseline integrates KL divergence directly into the reward:

$$R_i^{\mathrm{\prime }}=R_i-\beta \cdot \text{KL}({\pi }_{\theta }\mathrm{\mid }\mathrm{\mid }{\pi }_{\text{ref}})R\text{'}\_i\; =\; R\_i\; -\; \backslash beta\; \backslash cdot\; \backslash text\{KL\}(\backslash pi\_\backslash theta\; ||\; \backslash pi\_\{\backslash text\{ref\}\})$$

where $\beta$ is the KL divergence weight coefficient (corresponding to the parameter beta), and $\pi_{\text{ref}}$ is the reference policy.

Parameter Configuration

We can implement REINFORCE++ Baseline training by configuring the following parameters with GRPOTrainer:

--advantage_estimator reinforce_plus_plus
--scale_rewards batch
--kl_in_reward true

For training examples, please refer to this script

Key Parameter Descriptions

• --advantage_estimator: Selects the advantage estimation method

  • grpo (default): Uses the std of original rewards for normalization
  • reinforce_plus_plus: Uses the std of group-mean-subtracted rewards for normalization

• --kl_in_reward: Controls where the KL divergence regularization term is applied

  • false: KL divergence is an independent regularization term in the loss function (GRPO default)
  • true: KL divergence is subtracted directly from the reward (REINFORCE++ original implementation)

• --scale_rewards: Controls the normalization method

  • group (default): Intra-group normalization
  • batch: Global batch-level normalization (REINFORCE++ original implementation)
  • none: No normalization

• --num_generations: Number of samples generated per prompt ($G$)

• --beta: KL divergence regularization coefficient ($\beta$)

For other parameters, please refer to GRPO Parameters