Draft:Offline Reinforcement Learning for Drone Control

Abstract
This paper investigates the utilization of offline reinforcement learning for autonomous drone flight control, leveraging a pre-collected dataset encompassing various flight maneuvers such as takeoff, hovering, and circling at specific altitudes. To address the challenges posed by out-of-distribution data, we implemented a combination of on-policy Proximal Policy Optimization and off-policy algorithms, including Conservative Q-Learning integrated with Soft Actor-Critic, alongside Implicit Q-Learning. The effectiveness of these models was evaluated within a Python-based simulation environment. Our empirical results demonstrate that while the RL-generated policies closely approximate the offline dataset in numerical terms, they exhibit significant difficulties in successfully navigating and controlling the drone in the simulation. These findings underscore the complexities involved in applying offline RL to real-world drone operations and highlight the necessity for further refinement in bridging the gap between offline training and practical deployment.

Keywords
Offline Reinforcement Learning, Drone Control, CQL, SAC, IQL

Introduction
The rapid advancement in drone technology has opened new horizons for various applications, ranging from surveillance and delivery services to agricultural monitoring and disaster management. However, achieving autonomous and reliable drone flight control remains a significant challenge. Autonomous drones need to perform complex maneuvers such as takeoff, hovering, and precise navigation without human intervention. This paper explores offline reinforcement learning (RL) as a potential solution to enhance drone autonomy by leveraging pre-collected flight data. The ultimate long-term goal of this research is to develop a robust and efficient autonomous drone control system capable of operating in diverse environments and under various conditions, minimizing the need for real-time human control and adapting to different flight scenarios based on previously collected data.

Recent advancements in RL, such as Proximal Policy Optimization (PPO) and Soft Actor-Critic (SAC), have achieved notable success in various domains. However, these methods often struggle with out-of-distribution (OOD) data when applied to offline datasets. Despite significant contributions from researchers, the gap between current capabilities and the ultimate goal of reliable, autonomous drone flight remains. This paper aims to address the limitations of existing offline RL methods by investigating Conservative Q-Learning (CQL) combined with SAC and exploring Implicit Q-Learning (IQL) to develop a more robust RL approach that can effectively handle OOD data and improve policy learning from static datasets. Our contribution includes a detailed analysis and implementation of CQL, SAC, and IQL methods for drone flight control, evaluated in a Python-based simulation environment to highlight their strengths and limitations. This study focuses on simulation-based evaluations using pre-collected drone flight data, assuming the availability of high-quality data and computational feasibility of RL algorithms in simulation environments. This study aims to integrate Conservative Q-Learning (CQL) with Soft Actor-Critic (SAC) to handle out-of-distribution (OOD) issues in offline RL. It also investigates the performance differences between CQL, SAC, and Implicit Q-Learning (IQL) in drone flight control tasks. Furthermore, it examines the extent to which these methods improve the reliability and efficiency of autonomous drone operations in simulation.

State of the Art
The field of reinforcement learning has seen significant advancements over the past decade, particularly in developing algorithms capable of learning from both online and offline data. Various methods have been proposed to tackle the challenges associated with RL, such as data efficiency, stability, and robustness.

Proximal Policy Optimization (PPO)
PPO is a popular on-policy RL algorithm that alternates between sampling data from the environment and optimizing a surrogate objective function using stochastic gradient ascent. PPO has demonstrated superior performance on a variety of benchmark tasks, including robotic locomotion and Atari games. It strikes a balance between sample complexity, implementation simplicity, and wall-time performance .

Soft Actor-Critic (SAC)
SAC is an off-policy algorithm known for its sample efficiency and stability. It incorporates the maximum entropy framework to balance exploration and exploitation by encouraging policies to explore more widely. SAC has achieved state-of-the-art results in continuous control tasks and is widely adopted in various RL applications .

Conservative Q-Learning (CQL)
CQL addresses the overestimation bias commonly found in off-policy RL algorithms by learning a conservative Q-function. This ensures that the expected value of the policy under the learned Q-function lower-bounds its true value, thereby mitigating the risk of overestimation due to out-of-distribution (OOD) data. CQL has shown promise in improving policy performance, particularly in offline settings .

Implicit Q-Learning (IQL)
IQL is another off-policy algorithm designed to handle the challenges of offline RL. IQL learns value functions implicitly without directly estimating them, which helps in dealing with the discrepancies between the offline dataset and the learned policy. This method has been effective in reducing overestimation and improving policy robustness in offline settings .

Challenges and Gaps
Despite the advancements, several challenges remain in achieving the ultimate goal of reliable and efficient autonomous drone flight. Current methods, while effective in controlled environments, often struggle with real-world applicability due to issues such as data distribution shifts, policy generalization, and computational complexity. Bridging these gaps requires further research and the development of more robust algorithms that can handle the inherent uncertainties in offline RL scenarios.

Problem Statement
Despite significant advancements in reinforcement learning for autonomous systems, there remains a substantial gap in effectively leveraging offline RL for drone flight control. The primary challenge lies in addressing the OOD issues that arise when training models on pre-collected, static datasets. This problem is particularly critical in scenarios where real-world exploration is costly or dangerous, but a wealth of historical data is available.

This research will focus on integrating CQL with SAC and exploring the potential of IQL. The objective is to develop robust RL approaches that can effectively handle OOD data, improve policy learning from static datasets, and enhance the practical applicability of RL in autonomous drone control.

This study will address the following questions:
 * 1) How can CQL be effectively integrated with SAC to handle OOD issues in offline RL for drone flight control?
 * 2) What are the comparative performance differences between CQL, SAC, and IQL in controlling drones under various flight scenarios?
 * 3) To what extent do the integrated RL methods improve the reliability and efficiency of autonomous drone operations in a simulated environment?
 * 4) What are the limitations of the proposed methods, and how can they be addressed in future research?
 * 5) How does the complexity of the data distribution affect the performance and generalization of the learned policies?

Methodology
This study employs an experimental approach to evaluate the applicability of existing reinforcement learning theories to drone flight control. Specifically, we will test whether state-of-the-art RL algorithms can effectively control drones using pre-collected flight data in a simulated environment.

Data Collection and Preparation
We collected drone flight data using pre-implemented cascaded PID position controllers. The observation set for the agent includes the observation $$ s_t = [x_t^T, e_t^T, a_{t-1}^T]^T \in \mathbb{R}^{20} $$, containing the drone state vector $$ x \in \mathbb{R}^{13} $$. For the action set, it includes abstract, possibly high-level commands transformed by the control structure into the corresponding motor command $$ u \in U $$ in dimension $$ a \in \mathbb{R}^{4} $$ .

Model Implementation for CQL Combined with SAC
To implement the CQL and SAC model, we start with the key equations for both algorithms.


 * 1. Equations for CQL:**

CQL addresses overestimation error by minimizing action-values under the current policy and maximizing values under the data distribution to handle underestimation issues. The key objective in CQL is to minimize the following loss:

$$ \mathcal{L}_{\text{CQL}} = \min_Q \max_\mu \alpha \mathbb{E}_{(s, a) \sim \mu} [Q(s, a)] - \alpha \mathbb{E}_{(s, a) \sim \pi_{\beta}} [Q(s, a)] + \frac{1}{2} \mathbb{E}_{(s, a, s') \sim \mathcal{D}} \left[ \left( Q(s, a) - \hat{B}^{\pi} Q(s, a) \right)^2 \right] $$

This loss function penalizes the Q-values of actions not present in the dataset $$ \mathcal{D} $$, ensuring that the expected value of a policy under the learned Q-function serves as a lower bound to its true value.


 * 2. Equations for SAC:**

SAC is an off-policy RL algorithm that optimizes both the policy and Q-value function with the maximum entropy objective, which encourages exploration of actions not seen in the dataset. The key equations are:

$$ J_Q(\theta) = \mathbb{E}_{(s_t, a_t) \sim \mathcal{D}} \left[ \frac{1}{2} \left( Q_\theta(s_t, a_t) - \hat{Q}(s_t, a_t) \right)^2 \right] $$

where the target value $$ \hat{Q}(s_t, a_t) $$ is defined as:

$$ \hat{Q}(s_t, a_t) = r(s_t, a_t) + \gamma \mathbb{E}_{s_{t+1} \sim p} \left[ V_{\psi'}(s_{t+1}) \right] $$

The value function is trained to minimize the squared residual error:

$$ J_V(\psi) = \mathbb{E}_{s_t \sim \mathcal{D}} \left[ \frac{1}{2} \left( V_\psi(s_t) - \mathbb{E}_{a_t \sim \pi_\phi} \left[ Q_\theta(s_t, a_t) - \log \pi_\phi(a_t|s_t) \right] \right)^2 \right] $$

The policy is optimized by minimizing the expected KL-divergence:

$$ J_\pi(\phi) = \mathbb{E}_{s_t \sim \mathcal{D}} \left[ \text{KL} \left( \pi_\phi(\cdot|s_t) \| \exp(Q_\theta(s_t, \cdot))/Z_\theta(s_t) \right) \right] $$

This includes the reparameterization trick for lower variance gradient estimation:

$$ a_t = f_\phi(\epsilon_t; s_t) $$

Finally the objective for the maximum entropy reinforcement learning:

$$ J(\pi) = \sum_{t=0}^\infty \mathbb{E}_{(s_t, a_t) \sim \rho_\pi} \left[ \sum_{l=t}^\infty \gamma^{l-t} \mathbb{E}_{s_l \sim p, a_l \sim \pi} [r(s_t, a_t) + \alpha H(\pi(\cdot|s_t))|s_t, a_t] \right] $$


 * 3. CQL Combined with SAC:**

Combining these algorithms involves using the conservative Q-values from CQL within the SAC framework to update the policy and value functions.

The core algorithm can be described by the following loss function:

$$ \mathcal{L}(\theta_i) = \alpha \mathbb{E}_{s_t \sim \mathcal{D}} \left[\log{\sum_a \exp{Q_{\theta_i}(s_t, a)}} - \mathbb{E}_{a \sim \mathcal{D}} \big[Q_{\theta_i}(s_t, a)\big] - \tau \right] + \mathcal{L}_{\mathrm{SAC}}(\theta_i) $$

where $$ \alpha $$ is a value that is automatically adjusted using Lagrangian dual gradient descent, and $$ \tau $$ is a threshold parameter. When the difference in action values is less than $$ \tau $$, the $$ \alpha $$ will become smaller. Conversely, if the difference exceeds, the $$ \alpha $$ increases to strongly penalize the action values.

In continuous control:

$$ \log{\sum_a \exp{Q(s, a)}} \approx \log{\left(\frac{1}{2N} \sum_{a_i \sim \text{Unif}(a)}^N \left[\frac{\exp{Q(s, a_i)}}{\text{Unif}(a)}\right] + \frac{1}{2N} \sum_{a_i \sim \pi_\phi(a|s)}^N \left[\frac{\exp{Q(s, a_i)}}{\pi_\phi(a_i|s)}\right] \right)} $$

where $$ N $$ is the number of sampled actions.

Model Implementation for IQL
Instead of CQL, IQL is an innovative offline RL approach that avoids evaluating actions beyond those in the dataset, yet still allows the learned policy to significantly surpass the best behaviors in the data through generalization.

In IQL, there are three functions that need to be trained.

First, the state-value function is trained using expectile regression:

$$ L_V(\psi) = \mathbb{E}_{(s, a) \sim \mathcal{D}} [L_2^\tau (Q_\theta (s, a) - V_\psi (s))] $$

where $$ L_2^\tau (u) = |\tau - \mathbb{1}(u < 0)|u^2 $$.

Next, the Q-function is trained in conjunction with the state-value function to avoid querying actions:

$$ L_Q(\theta) = \mathbb{E}_{(s, a, r, s') \sim \mathcal{D}} [(r + \gamma V_\psi(s') - Q_\theta(s, a))^2] $$

Lastly, the policy function is trained using advantage weighted regression:

$$ L_\pi (\phi) = \mathbb{E}_{(s, a) \sim \mathcal{D}} [\exp(\beta (Q_\theta - V_\psi(s))) \log \pi_\phi(a|s)] $$

Experiments
In this experiment, we primarily focused on the changes in critic loss, actor loss, alpha loss, and alpha as the number of epochs increased. The results are shown in the figures below.

CQL Combined with SAC
The Conservative Q-Learning (CQL) model was configured with the following parameter settings:
 * Actor Encoder Factory:
 * Feature size: 13
 * Hidden units: [32, 32]
 * Activation: tanh
 * Critic Encoder Factory:
 * Hidden units: [300, 400]
 * Activation: tanh
 * Learning Rates:
 * Actor learning rate: 0.0001
 * Critic learning rate: 0.0001
 * Temperature learning rate: 0.0001
 * Batch Size: 500
 * Number of Steps: 500
 * Number of Epochs: 1000

IQL
The Implicit Q-Learning (IQL) model was configured with the following parameter settings:
 * Actor Encoder Factory:
 * Feature size: 13
 * Hidden units: [32, 32]
 * Activation: tanh
 * Critic Encoder Factory:
 * Hidden units: [32, 32]
 * Activation: tanh
 * Value Encoder Factory:
 * Hidden units: [32, 32]
 * Activation: tanh
 * Learning Rates:
 * Actor learning rate: 0.0001
 * Critic learning rate: 0.0001
 * Expectile: 0.71
 * Batch Size: 50000
 * Number of Steps: 500
 * Number of Epochs: 1000

Compared to Conservative Q-Learning (CQL), Implicit Q-Learning (IQL) leverages a state-value function, so we primarily focused on the changes in critic loss, actor loss, and value loss as the number of epochs increased. The results are shown in the figures below.

Discussion
In this section, we analyze and interpret the results presented in the previous chapter for Conservative Q-Learning (CQL) and Implicit Q-Learning (IQL). Each subsection focuses on different aspects of the performance metrics.

Analysis of CQL Performance

 * Critic Loss: The CQL critic loss initially rises rapidly due to the untrained Q-network, leading to large errors in Q-value predictions and significant parameter adjustments. After reaching a peak, the critic loss gradually decreases, indicating that the Q-network learns more accurate Q-value predictions from experiences and feedback. In the later stages of training, the critic loss decreases at a slower rate and stabilizes, showing the Q-network's convergence to an accurate representation of Q-values with smaller parameter adjustments.
 * Actor Loss: At the beginning of training, the actor loss rises rapidly as the policy network undergoes significant parameter adjustments. After reaching a peak, the actor loss gradually decreases, indicating that the policy network learns better strategies from the Q-network and environmental feedback. In the later stages of training, the actor loss decreases at a slower rate and stabilizes, showing the policy network's convergence to an optimal strategy with smaller parameter adjustments.
 * Alpha Loss: The alpha loss exhibits trends similar to the actor loss. Both losses initially increase sharply due to significant adjustments in the temperature parameter and policy network. After reaching a peak, the alpha loss declines steadily as the model becomes more confident in its policy decisions, reducing the need for large entropy adjustments.
 * Alpha: The alpha value shows a rapid initial adjustment followed by a steady decrease. This trend indicates the model's need to explore a wide range of actions and states initially, and then gradually gaining confidence in its policy, reducing the need for large entropy adjustments.

Analysis of IQL Performance

 * Critic Loss: The critic loss decreases steadily over the training steps, showing a more stable trend compared to the actor loss. This indicates that the Q-network learns to make more accurate value predictions, reducing prediction errors over time.
 * Actor Loss: The actor loss initially increases, reaches a peak, and then rapidly decreases. This sharp change might indicate convergence issues, with rapid fluctuations suggesting significant adjustments in the policy network. These fluctuations could be due to an overly aggressive learning rate or insufficient regularization.
 * Value Loss: The value loss mirrors the actor loss, showing a rapid increase to a peak followed by a sharp decrease. This symmetric pattern suggests substantial updates in both functions, potentially indicating convergence issues caused by aggressive learning rates or insufficient data smoothing.

General Observations
The convergence issues observed in IQL's actor and value loss trends might stem from several factors:
 * Learning Rate: An overly aggressive learning rate can cause large parameter updates, leading to instability.
 * Regularization: Insufficient regularization might lead to overfitting to noise in the training data, causing unstable learning.
 * Exploration-Exploitation Balance: An improper balance might cause erratic updates as the model switches between exploring new actions and exploiting known good actions.

Comparison of Stability and Convergence
The comparison of CQL and IQL indicates that while both algorithms improve their respective value predictions over time, CQL demonstrates more stable convergence patterns. In contrast, IQL exhibits significant fluctuations in actor and value loss, suggesting that further tuning of the learning rate and regularization might be necessary to achieve more stable convergence.

Overall Performance in Simulation
In the simulation, both CQL and IQL models were unable to successfully complete the flight tasks, despite having relatively low imitation errors after training. This discrepancy could be attributed to several potential factors:
 * Overfitting to Training Data: The models may have overfitted to the training data, learning specific patterns and noise present in the offline dataset rather than generalizable flight strategies. As a result, the models perform well on the training data but fail to adapt to the variability and unforeseen scenarios in the simulation environment.
 * Distributional Shift: There may be a significant distributional shift between the training data and the simulation environment. The offline training data might not fully capture the dynamics and variations present in the simulation, leading to poor generalization when the models encounter states and actions that were not adequately represented in the training set.
 * Model Complexity and Hyperparameters: The complexity of the models and the chosen hyperparameters might not be optimal for the given task. For instance, the learning rates, batch sizes, and network architectures could impact the model’s ability to learn effective policies. Aggressive learning rates or inadequate regularization might lead to unstable learning and poor performance in the simulation.
 * Exploration-Exploitation Balance: Both CQL and IQL aim to balance exploration and exploitation during training. However, if this balance is not appropriately maintained, the models might either overexploit the known data or overexplore suboptimal actions, leading to ineffective policies. The entropy terms and exploration strategies need to be carefully tuned to ensure robust learning.
 * Task-Specific Challenges: Comparing the simulation performance between the Circle task and the Take-off task reveals that the Circle task generally performed better. This could be attributed to the unique challenges associated with the Take-off task, such as ground effect issues. The ground effect can significantly impact the dynamics of the drone during take-off, making it a more complex maneuver to model and learn. The Circle task, being a more consistent and less dynamic maneuver, might have presented fewer challenges, leading to relatively better performance.

Conclusion
In this study, we evaluated the performance of Conservative Q-Learning (CQL) and Implicit Q-Learning (IQL) models on various drone flight tasks, including take-off and circle maneuvers. Despite achieving relatively low imitation errors during offline training, both models struggled to successfully complete the flight tasks in simulation. We propose several potential reasons for this discrepancy.

Our findings suggest that while CQL and IQL show promise, significant challenges remain in transferring learned policies from offline training to real-world-like environments. Improving the generalization and robustness of reinforcement learning models requires addressing issues such as overfitting, distributional shift, data quality, model complexity, simulation fidelity, and task-specific challenges.

Future Work
Future work should focus on enhancing the quality and diversity of training data, optimizing model hyperparameters, and improving the fidelity of simulation environments. Additionally, further research into handling task-specific challenges, such as ground effects in drone take-off, will be crucial for developing more robust and effective reinforcement learning models for real-world applications.

We also propose combining IQL with Soft Actor-Critic (SAC) to address the shortcomings of IQL in terms of exploration and its convergence and stability issues. By integrating the efficient exploration capabilities of SAC with the advantages of IQL, we aim to develop a hybrid model that can achieve better performance and robustness in complex environments. This approach could help to balance the trade-off between exploration and exploitation more effectively and enhance the overall learning stability.