torchrl.modules.mcts.UCB1TunedScore

class torchrl.modules.mcts.UCB1TunedScore(*args, **kwargs)

Computes the UCB1-Tuned score for MCTS, using variance estimation.

UCB1-Tuned is an enhancement of the UCB1 algorithm that incorporates an estimate of the variance of rewards for each action. This allows for a more refined balance between exploration and exploitation, potentially leading to better performance, especially when reward variances differ significantly across actions.

The score for an action i is calculated as: score_i = avg_reward_i + sqrt(log(N) / N_i * min(0.25, V_i))

The variance estimate V_i for action i is calculated as: V_i = (sum_squared_rewards_i / N_i) - avg_reward_i^2 + sqrt(exploration_constant * log(N) / N_i)

Where: - avg_reward_i: Average reward obtained from action i. - N_i: Number of times action i has been visited. - N: Total number of times the parent node has been visited. - sum_squared_rewards_i: Sum of the squares of rewards received from action i. - exploration_constant: A constant used in the bias correction term of V_i.

Auer et al. (2002) suggest a value of 2.0 for rewards in the range [0,1].

• The term min(0.25, V_i) implies that rewards are scaled to [0, 1], as 0.25 is the maximum variance for a distribution in this range (e.g., Bernoulli(0.5)).

Reference: “Finite-time Analysis of the Multiarmed Bandit Problem” (Auer, Cesa-Bianchi, Fischer, 2002).

Parameters:

• exploration_constant (float, optional) – The constant C used in the bias correction term for the variance estimate V_i. Defaults to 2.0, as suggested for rewards in [0,1].

• win_count_key (NestedKey, optional) – Key for the tensor in the input TensorDictBase containing the sum of rewards for each action (Q_i * N_i). Defaults to “win_count”.

• visits_key (NestedKey, optional) – Key for the tensor containing the visit count for each action (N_i). Defaults to “visits”.

• total_visits_key (NestedKey, optional) – Key for the tensor (or scalar) representing the visit count of the parent node (N). Defaults to “total_visits”.

• sum_squared_rewards_key (NestedKey, optional) – Key for the tensor containing the sum of squared rewards received for each action. This is crucial for calculating the empirical variance. Defaults to “sum_squared_rewards”.

• score_key (NestedKey, optional) – Key where the calculated UCB1-Tuned scores will be stored in the output TensorDictBase. Defaults to “score”.

Input Keys:

• win_count_key (torch.Tensor): Sum of rewards for each action.

• visits_key (torch.Tensor): Visit counts for each action (N_i).

• total_visits_key (torch.Tensor): Parent node’s visit count (N).

• sum_squared_rewards_key (torch.Tensor): Sum of squared rewards for each action.

Output Keys:

• score_key (torch.Tensor): Calculated UCB1-Tuned scores for each action.

Important Notes:

• Unvisited Nodes: Actions with zero visits (visits_key is 0) are assigned a very large positive score to ensure they are selected for exploration.

• Reward Range: The min(0.25, V_i) term is theoretically most sound when rewards are normalized to the range [0, 1].

• Logarithm of N: log(N) (log of parent visits) is calculated using torch.log(torch.clamp(N, min=1.0)) to prevent issues with N=0 or N between 0 and 1.

__init__(*, win_count_key: NestedKey = 'win_count', visits_key: NestedKey = 'visits', total_visits_key: NestedKey = 'total_visits', sum_squared_rewards_key: NestedKey = 'sum_squared_rewards', score_key: NestedKey = 'score', exploration_constant: float = 2.0)

Initialize internal Module state, shared by both nn.Module and ScriptModule.

Methods

__init__(*[, win_count_key, visits_key, ...])	Initialize internal Module state, shared by both nn.Module and ScriptModule.
add_module(name, module)	Add a child module to the current module.
apply(fn)	Apply fn recursively to every submodule (as returned by .children()) as well as self.
bfloat16()	Casts all floating point parameters and buffers to bfloat16 datatype.
buffers([recurse])	Return an iterator over module buffers.
children()	Return an iterator over immediate children modules.
compile(*args, **kwargs)	Compile this Module's forward using torch.compile().
cpu()	Move all model parameters and buffers to the CPU.
cuda([device])	Move all model parameters and buffers to the GPU.
double()	Casts all floating point parameters and buffers to double datatype.
eval()	Set the module in evaluation mode.
extra_repr()	Return the extra representation of the module.
float()	Casts all floating point parameters and buffers to float datatype.
forward(node)	Define the computation performed at every call.
get_buffer(target)	Return the buffer given by target if it exists, otherwise throw an error.
get_extra_state()	Return any extra state to include in the module's state_dict.
get_parameter(target)	Return the parameter given by target if it exists, otherwise throw an error.
get_submodule(target)	Return the submodule given by target if it exists, otherwise throw an error.
half()	Casts all floating point parameters and buffers to half datatype.
ipu([device])	Move all model parameters and buffers to the IPU.
is_tdmodule_compatible(module)	Checks if a module is compatible with TensorDictModule API.
load_state_dict(state_dict[, strict, assign])	Copy parameters and buffers from state_dict into this module and its descendants.
modules()	Return an iterator over all modules in the network.
mtia([device])	Move all model parameters and buffers to the MTIA.
named_buffers([prefix, recurse, ...])	Return an iterator over module buffers, yielding both the name of the buffer as well as the buffer itself.
named_children()	Return an iterator over immediate children modules, yielding both the name of the module as well as the module itself.
named_modules([memo, prefix, remove_duplicate])	Return an iterator over all modules in the network, yielding both the name of the module as well as the module itself.
named_parameters([prefix, recurse, ...])	Return an iterator over module parameters, yielding both the name of the parameter as well as the parameter itself.
parameters([recurse])	Return an iterator over module parameters.
register_backward_hook(hook)	Register a backward hook on the module.
register_buffer(name, tensor[, persistent])	Add a buffer to the module.
register_forward_hook(hook, *[, prepend, ...])	Register a forward hook on the module.
register_forward_pre_hook(hook, *[, ...])	Register a forward pre-hook on the module.
register_full_backward_hook(hook[, prepend])	Register a backward hook on the module.
register_full_backward_pre_hook(hook[, prepend])	Register a backward pre-hook on the module.
register_load_state_dict_post_hook(hook)	Register a post-hook to be run after module's load_state_dict() is called.
register_load_state_dict_pre_hook(hook)	Register a pre-hook to be run before module's load_state_dict() is called.
register_module(name, module)	Alias for add_module().
register_parameter(name, param)	Add a parameter to the module.
register_state_dict_post_hook(hook)	Register a post-hook for the state_dict() method.
register_state_dict_pre_hook(hook)	Register a pre-hook for the state_dict() method.
requires_grad_([requires_grad])	Change if autograd should record operations on parameters in this module.
reset_out_keys()	Resets the out_keys attribute to its orignal value.
reset_parameters_recursive([parameters])	Recursively reset the parameters of the module and its children.
select_out_keys(*out_keys)	Selects the keys that will be found in the output tensordict.
set_extra_state(state)	Set extra state contained in the loaded state_dict.
set_submodule(target, module[, strict])	Set the submodule given by target if it exists, otherwise throw an error.
share_memory()	See torch.Tensor.share_memory_().
state_dict(*args[, destination, prefix, ...])	Return a dictionary containing references to the whole state of the module.
to(*args, **kwargs)	Move and/or cast the parameters and buffers.
to_empty(*, device[, recurse])	Move the parameters and buffers to the specified device without copying storage.
train([mode])	Set the module in training mode.
type(dst_type)	Casts all parameters and buffers to dst_type.
xpu([device])	Move all model parameters and buffers to the XPU.
zero_grad([set_to_none])	Reset gradients of all model parameters.

Attributes

T_destination
call_super_init
dump_patches
in_keys
out_keys
out_keys_source
training