Given the following case study, identify the likely cause of the training instability and propose a specific adjustment to the objective function to resolve it. Explain your reasoning.

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The PPO-Clip training method utilizes a composite objective function that integrates a policy divergence penalty with the clipped surrogate objective ($U_{\text{clip}}$). The formula is expressed as: $$ U_{\text{ppo-clip}}(\tau; \theta) = U_{\text{clip}}(\tau; \theta) - \beta \text{Penalty} $$ In this equation, the hyperparameter $\beta$ serves as the weight for the penalty term, controlling its influence on the overall objective.

Composite Objective for PPO-Clip

In a policy optimization method, a composite objective function is used, defined as `Objective = Clipped_Surrogate_Objective - β * Divergence_Penalty`. This function balances maximizing the primary objective with a penalty for how much the policy changes. What is the most likely consequence of setting the hyperparameter `β` to a very high value?

Stabilizing Policy Optimization Training

Consider the following composite objective function used in a policy optimization algorithm: $$ U_{\text{composite}} = U_{\text{surrogate}} - \beta \cdot \text{Penalty} $$ Explain the fundamental trade-off that the hyperparameter `β` is designed to manage during the training process.

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