# DRO

DRO ( [Richemond et al., 2024](https://arxiv.org/abs/2405.19107); [Kimi Team et al., 2025](https://arxiv.org/abs/2501.12599)) is a general off-policy (and even offline) reinforcement learning method that uses a quadratic penalty term to constrain the policy update. Notice that this loss uses a different (soft) formulation of the advantage estimation, which needs to be implemented on the client side.

The DRO objective is:

LDRO(θ)=Ex∼q\[log⁡pθ(x)⋅A(x)−12β(log⁡pθ(x)q(x))2\]
\mathcal{L}\_{\text{DRO}}(\theta) = \mathbb{E}\_{x \sim q}\left\[\log p\_\theta(x) \cdot A(x) - \frac{1}{2}\beta \left(\log \frac{p\_\theta(x)}{q(x)}\right)^2\right\]
LDRO​(θ)=Ex∼q​\[logpθ​(x)⋅A(x)−21​β(logq(x)pθ​(x)​)2\]

This is implemented as:

```
# Compute quadratic penalty term
quadratic_term = (target_logprobs - sampling_logprobs) ** 2
# Compute DRO objective
dro_objective = target_logprobs * advantages - 0.5 * beta * quadratic_term
# DRO loss is negative of objective
loss = -dro_objective.sum()
```

**Input tensors:**

- `target_tokens: array[(N,), int]` — Target token IDs (from the sampler qqq)
- `logprobs: array[(N,), float]` — `sampling_logprobs` for the tokens
- `advantages: array[(N,), float]` — Advantage values for RL

**Output tensors:**

- `logprobs: array[(N,), float]` — `target_logprobs` for the tokens

**Output diagnostics:**

- `loss:sum` (scalar) — Sum of DRO losses

## Custom beta

```
fwd_bwd_future = await training_client.forward_backward_async(
    data=data,
    loss_fn="dro",
    loss_fn_config={"beta": 0.05}
)
fwd_bwd_result = await fwd_bwd_future.result_async()
```