Monte Carlo Gradient Estimation

def score_function_jacobians(
    function, 
    params, 
    dist_builder, 
    rng, 
    num_samples
):
    """
    Score function gradient estimation (REINFORCE).
    
    Args:
        function: Function f(x) for gradient estimation
        params: Parameters for constructing the distribution  
        dist_builder: Constructor for building distributions from parameters
        rng: PRNGKey for random sampling
        num_samples: Number of samples for gradient computation
    
    Returns:
        Sequence[chex.Array]: Tuple of jacobian vectors with shape num_samples x param.shape
    """

def pathwise_jacobians(
    function, 
    params, 
    dist_builder, 
    rng, 
    num_samples
):
    """
    Pathwise gradient estimation (reparameterization trick).
    
    Args:
        function: Function f(x) for gradient estimation (must be differentiable)
        params: Parameters for constructing the distribution
        dist_builder: Constructor for building distributions from parameters
        rng: PRNGKey for random sampling
        num_samples: Number of samples for gradient computation
    
    Returns:
        Sequence[chex.Array]: Tuple of jacobian vectors with shape num_samples x param.shape
    """

def measure_valued_jacobians(
    function, 
    params, 
    dist_builder, 
    rng, 
    num_samples, 
    coupling=True
):
    """
    Measure-valued gradient estimation.
    
    Args:
        function: Function f(x) for gradient estimation
        params: Parameters for constructing the distribution
        dist_builder: Constructor for building distributions from parameters
        rng: PRNGKey for random sampling
        num_samples: Number of samples for gradient computation
        coupling: Whether to use coupling for positive/negative samples (default: True)
    
    Returns:
        Sequence[chex.Array]: Tuple of jacobian vectors with shape num_samples x param.shape
    """

def moving_avg_baseline(
    function, 
    decay=0.99, 
    zero_debias=True, 
    use_decay_early_training_heuristic=True
):
    """
    Moving average baseline control variate.
    
    Args:
        function: Function for which to compute the control variate
        decay: Decay rate for the moving average (default: 0.99)
        zero_debias: Whether to use zero debiasing (default: True)
        use_decay_early_training_heuristic: Whether to use early training heuristic (default: True)
    
    Returns:
        ControlVariate: Tuple of three functions for computing control variate
    """

def control_delta_method(function):
    """
    Control delta covariant method control variate.
    
    Args:
        function: The function for which to compute the control variate
    
    Returns:
        ControlVariate: Tuple of three functions for computing control variate
    """

def control_variates_jacobians(
    function,
    control_variate_from_function,
    grad_estimator,
    params,
    dist_builder,
    rng,
    num_samples,
    control_variate_state=None,
    estimate_cv_coeffs=False,
    estimate_cv_coeffs_num_samples=20
):
    """
    Gradient estimation using control variates for variance reduction.
    
    Args:
        function: Function f(x) for which to estimate gradients
        control_variate_from_function: The control variate to use
        grad_estimator: The gradient estimator to compute gradients
        params: Parameters for constructing the distribution
        dist_builder: Constructor that builds a distribution from parameters
        rng: PRNGKey for random sampling
        num_samples: Number of samples for gradient computation
        control_variate_state: State of the control variate (optional)
        estimate_cv_coeffs: Whether to estimate optimal coefficients
        estimate_cv_coeffs_num_samples: Number of samples for coefficient estimation
    
    Returns:
        tuple[Sequence[chex.Array], CvState]: Jacobians and updated control variate state
    """

import optax
import jax
import jax.numpy as jnp

# Example: Score function gradient estimation
def objective_function(x):
    return jnp.sum(x**2)

# Parameters for a Gaussian distribution
params = {'mean': jnp.array([1.0, 2.0]), 'log_std': jnp.array([0.0, 0.0])}

def gaussian_builder(mean, log_std):
    return tfd.Normal(loc=mean, scale=jnp.exp(log_std))

rng = jax.random.PRNGKey(42)
num_samples = 1000

# Use score function estimator
gradients = optax.monte_carlo.score_function_jacobians(
    function=objective_function,
    params=params,
    dist_builder=gaussian_builder,
    rng=rng,
    num_samples=num_samples
)

# Use pathwise estimator (requires differentiable function)
gradients_pathwise = optax.monte_carlo.pathwise_jacobians(
    function=objective_function,
    params=params,
    dist_builder=gaussian_builder,
    rng=rng,
    num_samples=num_samples
)

import optax.monte_carlo
# or
from optax.monte_carlo import (
    score_function_jacobians,
    pathwise_jacobians,
    measure_valued_jacobians,
    moving_avg_baseline,
    control_delta_method,
    control_variates_jacobians
)

# Control variate types
ControlVariate = tuple[
    Callable,  # Control variate computation function
    Callable,  # Expected value function
    Callable   # State update function
]

CvState = Any  # Control variate state