# Import necessary libraries
from transformers import AutoTokenizer, TFBertModel
import tensorflow_probability as tfp
import optax
from flax.training import train_state
from opt_einsum import jit
from typing import Callable, List, Optional

# Load pre-trained GPT2 model using Hugging Face Transformers library
tokenizer = AutoTokenizer.from_pretrained('gpt2')
model = TFBertModel.from_pretrained('gpt2', checkpoint='last')

# Define function to calculate loss and optimize parameters for FlaxOPTForCausalLM tool
def train(params, inputs):
    # Convert input text into tokenized list using Hugging Face Transformers library's tokenizer
    tokens = tokenizer.batch_encode_plus(inputs['input'], padding=True, truncation=True)
    # Calculate loss function based on how closely predicted output matches actual output
    with tfp.autoregressive:
        logits = model(tokens['input_ids'])[0]
        target_logits = tokens['labels'][:, 1:] - tokens['labels'][:, :-1] # Calculate difference between target and predicted outputs for each token
        loss = tfp.math.softmax_cross_entropy(logits, target_logits)
    return jit(loss)(params)

# Define function to update parameters using FlaxOPTForCausalLM tool
def optimize(state, inputs):
    # Calculate loss and gradients for current input text
    loss = train(state.params, inputs)
    grads = tfp.math.gradient(loss, state.params)
    # Update parameters using FlaxOPTForCausalLM tool's optimizer function
    return optax.adam().update(state, grads)

# Load training data and split into batches for optimization
train_data = [('Input text 1', 'Output text 1'), ('Input text 2', 'Output text 2')]
batches = list(zip(*[iter(train_data)]*2)) # Split input and output texts into separate lists for easier processing
batch_size = 32
num_epochs = 50
learning_rate = 1e-4
optimizer = optax.adam()
state = train_state.TrainState.create(apply_fn=optimize, params=model.trainable_params) # Create initial training state with FlaxOPTForCausalLM tool's optimizer function and pre-trained GPT2 model's parameters
for epoch in range(num_epochs):
    for batch in batches:
        input_text, output_text = zip(*batch)[0] # Extract input text from current training batch
        target_output_text = list(zip(*[iter(train_data)]*2))[1][input_text.index(input_text):input_text.index(input_text)+len(output_text)].tolist()[0] # Extract corresponding output text from training data based on input text's index
        inputs = {'input': tokenizer.batch_encode_plus([input_text], padding=True, truncation=True)} # Convert input text into tokenized list using Hugging Face Transformers library's tokenizer and add padding/truncation as needed
        state = optimize(state, inputs) # Update parameters using FlaxOPTForCausalLM tool's optimizer function for current training batch
    print('Epoch {} complete'.format(epoch+1)) # Print progress message after each epoch of optimization

# Explanation:
# - The script starts by importing necessary libraries, including the Hugging Face Transformers library, TensorFlow Probability, Optax, and Flax.
# - The pre-trained GPT2 model is loaded using the AutoTokenizer and TFBertModel classes from the Transformers library.
# - The train function is defined to calculate the loss and optimize parameters for the FlaxOPTForCausalLM tool. The input text is tokenized using the tokenizer from the Transformers library, and the loss is calculated based on the difference between the predicted and target outputs.
# - The optimize function is defined to update the parameters using the FlaxOPTForCausalLM tool's optimizer function. The loss and gradients are calculated using the train function, and the parameters are updated using the Optax library.
# - The training data is loaded and split into batches for optimization.
# - The state is initialized with the FlaxOPTForCausalLM tool's optimizer function and the pre-trained GPT2 model's parameters.
# - The training loop runs for the specified number of epochs, and for each epoch, the batches are iterated through. The input and output texts are extracted from the current batch, and the corresponding target output text is retrieved from the training data. The input text is tokenized and passed into the optimize function to update the parameters.
# - After each epoch, a progress message is printed.