2 Output Layer Dense (2 units), activation='linear' (for t+1 and t+2) The optimization was conducted using the Adam optimizer with an initial learning rate of 10-3 and Mean Squared Error (MSE) as the objective loss function. To ensure computational efficiency and prevent overfitting, training was performed with a batch size of 128 samples for a maximum of 50 epochs, governed by an Early Stopping mechanism with a patience of 20 epochs on validation loss. The predictive performance of the LSTM architectures was quantitatively assessed across each discrete forecast horizon ℎ ∈{1,2}, corresponding to 5-minute and 10minute lead times. Performance was measured using three statistical indicators: Mean Absolute Error (MAE), representing the average error magnitude in microns; Root Mean Squared Error (RMSE), which penalizes significant outliers to ensure process stability; and the Coefficient of Determination R2, which quantifies the proportion of process variance captured by the model. This per-horizon approach rigorously monitors the temporal decay of predictive accuracy as the forecast lead time increases. 3.4. Reinforcement Learning Methodology The grinding circuit control problem can be formalized as a Partially Observable Markov Decision Process (POMDP), acknowledging that the full internal state of the process cannot be directly measured through available plant sensors. Instead, the control policy operates on observable variables (e.g., P80, power draw, feed rate), which provide only a partial representation of the true system state. This partial observability justifies the use of temporal models, such as LSTM networks, to implicitly capture hidden dynamics and approximate the underlying Markovian structure through historical information This work addresses the automatic control of a grinding circuit using an offline reinforcement learning (RL) approach. The goal is to maintain the product particle size (P80) at a target of 160 µm within a tolerance band of ±10 µm, while adjusting manipulated variables. The RL model follows the variable classification framework proposed by Hodouin (2011) explained before. The temporal state is captured using a sliding window of 6 timesteps across all features. The LSTM autoregressive model selected of previous stage is integrated as a Differentiable Surrogate Environment, which serves as the "world model" for the RL agent. The model is differentiable end-to-end, meaning gradients can flow from the predicted P80 back through the LSTM to the action inputs. This enables model-based policy gradient training without plant interaction. The implemented RL agent follows a Differentiable Actor-Critic (DAC) model-based framework as shown in Table 2, where a deterministic policy is trained using a differentiable LSTM surrogate that represents the grinding circuit dynamics. The actor optimizes control actions by executing a 10-step forward rollout through the LSTM-based environment and minimizing the negative predicted cumulative reward via backpropagation, enabling gradients to propagate through the surrogate transition model. A single critic network estimates the value of the predicted return; however, unlike conventional actor-critic methods, no replay-based temporal-difference learning is performed, as optimization is driven by model-based trajectory gradients. The training procedure consists of 300 iterations with a batch size of 64, employing a discount factor of γ =
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