# A New AI Approach by Acquisition of Characteristics in Human Decision-Making Process
## 3 Challenges in Imitation Learning  
IL as learning from demonstration or apprenticeship learning is generally mathematically formulated within the framework of reinforcement learning [39]. The goal of imitation learning is to enable an agent to mimic expert behavior by learning from observed demonstrations. The following notations are used:  
* State space: \(S\), set of all possible states.
* Action space: \(A\), set of all possible actions.
* Reward function: \(R:S\times A\rightarrow\mathbb{R}\), defines the immediate reward for taking an action in a state.
* Demonstration dataset: \(D=\{(s_{1},a_{1}),(s_{2},a_{2}),\dots,(s_{t},a_{t})\}\), set of state-action pairs from expert demonstrations.
* Policy: \(\pi:S\to A\), agent's policy mapping states to actions.  
The objective of IL is to learn a policy \(\pi\) that mimics the expert's behavior, as demonstrated in \(D\), where the aim is to find a policy \(\pi\) that maximizes the expected cumulative reward, like RL but without direct interaction with the environment. In the BC approach, a policy \(\pi\) is directly learned that maps state \(s\) to action \(a\) based on the observed demonstrations [40]. The learning objective of BC can be formulated as minimizing the expected loss between the actions predicted by \(\pi\) and the actions in the demonstration dataset \(D\) according to  
\[min_{\pi}\mathbb{E}_{s\sim D}[loss(\pi(s),a)]. \tag{1}\]  
Here, \(loss\) is a suitable loss function (e.g., mean squared error or cross-entropy) that measures the discrepancy between the predicted action \(\pi(s)\) and demonstrated action \(a\). In the inverse reinforcement learning (IRL) approach, the agent infers the underlying reward function \(R\) from the expert's behavior and then learns a policy \(\pi\) that maximizes this inferred reward [41]. The learning process involves estimating the reward function \(R\) based on the observed demonstrations and then optimizing the policy \(\pi\) to maximize the expected cumulative reward under this reward function according to  
\[max_{\pi}\sum_{t=1}^{T}\mathbb{E}_{S_{t}\sim p(.)}[R(s_{t},\pi(s_{t})], \tag{2}\]  
where \(p(.)\) is the distribution over states encountered during the execution of policy \(\pi\).  
Considering the training and optimization in IL methods, two major trends can be mentioned: the supervised learning approach and iterative improvement. BC can be framed as a supervised learning problem, where the policy \(\pi\) is learned using supervised learning techniques (e.g., neural networks) to minimize the prediction error between \(\pi(s)\) and \(a\) from \(D\). Iterative approaches, such as policy iteration or gradient-based optimization methods (e.g., policy gradient), can be employed to iteratively update the policy \(\pi\) to maximize the expected reward based on the observed demonstrations.  
Three major challenges can be considered in relation to IL, which are as follows [6, 10, 42]:  
* Generalization: one key challenge in imitation learning is generalizing the learned policy \(\pi\) to new, unseen situations that may differ from the demonstrations;
* Distribution mismatch: the distribution of states encountered during the policy execution by the agent may differ from the distribution of states in the demonstration dataset \(D\), leading to challenges in effective learning;
* Bias and variance trade-off: balancing bias (due to approximation error) and variance (due to noisy demonstrations) is critical for successful imitation learning.  
Various techniques and algorithms can be applied to address challenges and achieve effective imitation learning. However, we believe the difficulty of environment dynamics that can be expressed with common sense problems is the major challenge with IL approaches, which cannot be solved due to their fundamental limitation of using an MDP.