jax.example_libraries.optimizers module — JAX documentation (original) (raw)

jax.example_libraries.optimizers module#

Examples of how to write optimizers with JAX.

You likely do not mean to import this module! The optimizers in this library are intended as examples only. If you are looking for a fully featured optimizer library, consider Optax.

This module contains some convenient optimizer definitions, specifically initialization and update functions, which can be used with ndarrays or arbitrarily-nested tuple/list/dicts of ndarrays.

An optimizer is modeled as an (init_fun, update_fun, get_params) triple of functions, where the component functions have these signatures:

init_fun(params)

Args: params: pytree representing the initial parameters.

Returns: A pytree representing the initial optimizer state, which includes the initial parameters and may also include auxiliary values like initial momentum. The optimizer state pytree structure generally differs from that of params.

update_fun(step, grads, opt_state)

Args: step: integer representing the step index. grads: a pytree with the same structure as get_params(opt_state) representing the gradients to be used in updating the optimizer state. opt_state: a pytree representing the optimizer state to be updated.

Returns: A pytree with the same structure as the opt_state argument representing the updated optimizer state.

get_params(opt_state)

Args: opt_state: pytree representing an optimizer state.

Returns: A pytree representing the parameters extracted from opt_state, such that the invariant params == get_params(init_fun(params)) holds true.

Notice that an optimizer implementation has a lot of flexibility in the form of opt_state: it just has to be a pytree of JaxTypes (so that it can be passed to the JAX transforms defined in api.py) and it has to be consumable by update_fun and get_params.

Example Usage:

opt_init, opt_update, get_params = optimizers.sgd(learning_rate) opt_state = opt_init(params)

def step(step, opt_state): value, grads = jax.value_and_grad(loss_fn)(get_params(opt_state)) opt_state = opt_update(step, grads, opt_state) return value, opt_state

for i in range(num_steps): value, opt_state = step(i, opt_state)

class jax.example_libraries.optimizers.JoinPoint(subtree)[source]#

Bases: object

Marks the boundary between two joined (nested) pytrees.

class jax.example_libraries.optimizers.Optimizer(init_fn, update_fn, params_fn)[source]#

Bases: NamedTuple

Parameters:

• init_fn (InitFn)
• update_fn (UpdateFn)
• params_fn (ParamsFn)

init_fn_: InitFn_#

Alias for field number 0

params_fn_: ParamsFn_#

Alias for field number 2

update_fn_: UpdateFn_#

Alias for field number 1

class jax.example_libraries.optimizers.OptimizerState(packed_state, tree_def, subtree_defs)#

Bases: tuple

packed_state#

Alias for field number 0

subtree_defs#

Alias for field number 2

tree_def#

Alias for field number 1

jax.example_libraries.optimizers.adagrad(step_size, momentum=0.9)[source]#

Construct optimizer triple for Adagrad.

Adaptive Subgradient Methods for Online Learning and Stochastic Optimization:http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf

Parameters:

• step_size – positive scalar, or a callable representing a step size schedule that maps the iteration index to a positive scalar.
• momentum – optional, a positive scalar value for momentum

Returns:

An (init_fun, update_fun, get_params) triple.

jax.example_libraries.optimizers.adam(step_size, b1=0.9, b2=0.999, eps=1e-08)[source]#

Construct optimizer triple for Adam.

Parameters:

• step_size – positive scalar, or a callable representing a step size schedule that maps the iteration index to a positive scalar.
• b1 – optional, a positive scalar value for beta_1, the exponential decay rate for the first moment estimates (default 0.9).
• b2 – optional, a positive scalar value for beta_2, the exponential decay rate for the second moment estimates (default 0.999).
• eps – optional, a positive scalar value for epsilon, a small constant for numerical stability (default 1e-8).

Returns:

An (init_fun, update_fun, get_params) triple.

jax.example_libraries.optimizers.adamax(step_size, b1=0.9, b2=0.999, eps=1e-08)[source]#

Construct optimizer triple for AdaMax (a variant of Adam based on infinity norm).

Parameters:

• step_size – positive scalar, or a callable representing a step size schedule that maps the iteration index to a positive scalar.
• b1 – optional, a positive scalar value for beta_1, the exponential decay rate for the first moment estimates (default 0.9).
• b2 – optional, a positive scalar value for beta_2, the exponential decay rate for the second moment estimates (default 0.999).
• eps – optional, a positive scalar value for epsilon, a small constant for numerical stability (default 1e-8).

Returns:

An (init_fun, update_fun, get_params) triple.

jax.example_libraries.optimizers.clip_grads(grad_tree, max_norm)[source]#

Clip gradients stored as a pytree of arrays to maximum norm max_norm.

jax.example_libraries.optimizers.constant(step_size)[source]#

Return type:

Schedule

jax.example_libraries.optimizers.exponential_decay(step_size, decay_steps, decay_rate)[source]#

jax.example_libraries.optimizers.inverse_time_decay(step_size, decay_steps, decay_rate, staircase=False)[source]#

jax.example_libraries.optimizers.l2_norm(tree)[source]#

Compute the l2 norm of a pytree of arrays. Useful for weight decay.

jax.example_libraries.optimizers.make_schedule(scalar_or_schedule)[source]#

Parameters:

scalar_or_schedule (float | Schedule)

Return type:

Schedule

jax.example_libraries.optimizers.momentum(step_size, mass)[source]#

Construct optimizer triple for SGD with momentum.

Parameters:

• step_size (Schedule) – positive scalar, or a callable representing a step size schedule that maps the iteration index to a positive scalar.
• mass (float) – positive scalar representing the momentum coefficient.

Returns:

An (init_fun, update_fun, get_params) triple.

jax.example_libraries.optimizers.nesterov(step_size, mass)[source]#

Construct optimizer triple for SGD with Nesterov momentum.

Parameters:

• step_size (Schedule) – positive scalar, or a callable representing a step size schedule that maps the iteration index to a positive scalar.
• mass (float) – positive scalar representing the momentum coefficient.

Returns:

An (init_fun, update_fun, get_params) triple.

jax.example_libraries.optimizers.optimizer(opt_maker)[source]#

Decorator to make an optimizer defined for arrays generalize to containers.

With this decorator, you can write init, update, and get_params functions that each operate only on single arrays, and convert them to corresponding functions that operate on pytrees of parameters. See the optimizers defined in optimizers.py for examples.

Parameters:

opt_maker (Callable _[_ _..._ _,_ tuple[ Callable [ [ Params ] , State ] , Callable [ [ Step , Updates , Params ] , Params ] , Callable [ [ State ] , Params ] ] ]) –

a function that returns an (init_fun, update_fun, get_params)triple of functions that might only work with ndarrays, as per

init_fun :: ndarray -> OptStatePytree ndarray update_fun :: OptStatePytree ndarray -> OptStatePytree ndarray get_params :: OptStatePytree ndarray -> ndarray

Returns:

An (init_fun, update_fun, get_params) triple of functions that work on arbitrary pytrees, as per

init_fun :: ParameterPytree ndarray -> OptimizerState update_fun :: OptimizerState -> OptimizerState get_params :: OptimizerState -> ParameterPytree ndarray

The OptimizerState pytree type used by the returned functions is isomorphic to ParameterPytree (OptStatePytree ndarray), but may store the state instead as e.g. a partially-flattened data structure for performance.

Return type:

Callable[…, Optimizer]

jax.example_libraries.optimizers.pack_optimizer_state(marked_pytree)[source]#

Converts a marked pytree to an OptimizerState.

The inverse of unpack_optimizer_state. Converts a marked pytree with the leaves of the outer pytree represented as JoinPoints back into an OptimizerState. This function is intended to be useful when deserializing optimizer states.

Parameters:

marked_pytree – A pytree containing JoinPoint leaves that hold more pytrees.

Returns:

An equivalent OptimizerState to the input argument.

jax.example_libraries.optimizers.piecewise_constant(boundaries, values)[source]#

Parameters:

• boundaries (Any)
• values (Any)

jax.example_libraries.optimizers.polynomial_decay(step_size, decay_steps, final_step_size, power=1.0)[source]#

jax.example_libraries.optimizers.rmsprop(step_size, gamma=0.9, eps=1e-08)[source]#

Construct optimizer triple for RMSProp.

Parameters:

step_size – positive scalar, or a callable representing a step size schedule that maps the iteration index to a positive scalar. gamma: Decay parameter. eps: Epsilon parameter.

Returns:

An (init_fun, update_fun, get_params) triple.

jax.example_libraries.optimizers.rmsprop_momentum(step_size, gamma=0.9, eps=1e-08, momentum=0.9)[source]#

Construct optimizer triple for RMSProp with momentum.

This optimizer is separate from the rmsprop optimizer because it needs to keep track of additional parameters.

Parameters:

• step_size – positive scalar, or a callable representing a step size schedule that maps the iteration index to a positive scalar.
• gamma – Decay parameter.
• eps – Epsilon parameter.
• momentum – Momentum parameter.

Returns:

An (init_fun, update_fun, get_params) triple.

jax.example_libraries.optimizers.sgd(step_size)[source]#

Construct optimizer triple for stochastic gradient descent.

Parameters:

step_size – positive scalar, or a callable representing a step size schedule that maps the iteration index to a positive scalar.

Returns:

An (init_fun, update_fun, get_params) triple.

jax.example_libraries.optimizers.sm3(step_size, momentum=0.9)[source]#

Construct optimizer triple for SM3.

Memory-Efficient Adaptive Optimization for Large-Scale Learning.https://arxiv.org/abs/1901.11150

Parameters:

• step_size – positive scalar, or a callable representing a step size schedule that maps the iteration index to a positive scalar.
• momentum – optional, a positive scalar value for momentum

Returns:

An (init_fun, update_fun, get_params) triple.

jax.example_libraries.optimizers.unpack_optimizer_state(opt_state)[source]#

Converts an OptimizerState to a marked pytree.

Converts an OptimizerState to a marked pytree with the leaves of the outer pytree represented as JoinPoints to avoid losing information. This function is intended to be useful when serializing optimizer states.

Parameters:

opt_state – An OptimizerState

Returns:

A pytree with JoinPoint leaves that contain a second level of pytrees.