How do you deal with multi-objective or conflicting rewards in RL?

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Reinforcement learning (RL) is a branch of machine learning that focuses on learning from trial and error, based on rewards and penalties. In many real-world problems, however, the rewards are not clear-cut, but rather depend on multiple objectives or trade-offs. For example, an autonomous vehicle may have to balance safety, speed, and fuel efficiency, while a recommender system may have to consider user satisfaction, diversity, and revenue. How do you deal with such multi-objective or conflicting rewards in RL? In this article, we will explore some of the challenges and solutions for this topic.

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Combine rewards creatively:

Utilize weighted sums to integrate multiple objectives into a single reward. Adjust the weights to reflect the importance of each goal, but be mindful that this approach might not fully capture conflicting objectives.### *Explore multi-objective optimization:Employ methods like scalarization or evolutionary algorithms to approximate the Pareto front. This helps in finding balanced policies that consider trade-offs without compromising on critical objectives.

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Daniel Zaldana

??LinkedIn Top Voice in Artificial…
Khushee Kapoor

UWaterloo | Master of Data Science and…

1 Reward function design

One of the first steps in RL is to define the reward function, which specifies how the agent is evaluated and motivated. A common approach is to use a scalar reward function, which combines the different objectives into a single value, such as a weighted sum or a utility function. However, this requires making assumptions and trade-offs about the relative importance and preferences of the objectives, which may not be easy or accurate. Moreover, a scalar reward function may not capture the diversity or complexity of the objectives, and may lead to suboptimal or biased policies.

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Daniel Zaldana

??LinkedIn Top Voice in Artificial Intelligence | Algorithms | Thought Leadership
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When choosing weights for different objectives, you’re making assumptions about their relative importance. The challenge here is that these assumptions can introduce bias, making the agent optimize in ways that don’t align with real-world goals. Often, your assumptions won't capture the full complexity of the environment, and the agent might gravitate toward suboptimal behavior. Example: In a hospital scheduling system, if you favor minimizing operational costs over staff well-being, the system might schedule doctors with long, exhausting shifts, leading to burnout and poorer patient outcomes over time. Balancing these objectives requires a nuanced understanding of long-term trade-offs.

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Khushee Kapoor

UWaterloo | Master of Data Science and Artificial Intelligence (Co-op) | LinkedIn Top Voice for Data Science | Amongst the Top 0.5% Data Scientists on Kaggle
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Weighted Sum: Combine multiple objectives into a single reward using weighted sums. Adjusting the weights allows you to balance the importance of different objectives, but it might not handle conflicting goals well. Scalarization Techniques: Transform multiple objectives into a single objective using scalarization functions, like weighted sum, weighted product, or other mathematical formulations. This simplifies the problem but may not capture the true trade-offs between conflicting goals. Reward Shaping: Use reward shaping to guide the learning process. Add auxiliary rewards that encourage desirable behavior or discourage unwanted actions. Be cautious to avoid unintentionally introducing new conflicts or biases.

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Dr. Mario Javier Pérez Rivas

Director of AI and Cloud Infrastructure Services
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In multi-objective reinforcement learning (RL), crafting reward functions is challenging due to the diversity of goals, like balancing efficiency in smart grids or achieving speed in robotics. Scalar rewards often oversimplify, while methods like multi-objective rewards and Pareto optimization offer nuanced approaches. Techniques like hierarchical RL simplify complex tasks, and curriculum learning introduces objectives progressively. Multi-agent RL uses different agents for specific goals in complex systems. Balancing exploration with exploitation, ensuring scalability, and maintaining interpretability are crucial. These strategies enable effective navigation of the complexities in multi-objective RL scenarios.

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Arta Asadi

Machine Learning Engineer@ Smart Land Solutions
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Normalization and also knowledge of the nature of the reward/penalty are key. Some times you need to combine a risk with a reward! So you can normalize them, and subtract from a base number like 0 or 1.

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2 Reward function estimation

Another challenge in RL is to estimate the reward function from data, especially when the objectives are not directly observable or measurable. For example, in inverse reinforcement learning (IRL), the goal is to infer the reward function from the observed behavior of an expert or a human. However, this may be difficult or unreliable, as the behavior may be noisy, inconsistent, or incomplete. Moreover, the reward function may not be unique or well-defined, as different agents may have different preferences or goals. To address this challenge, some methods use multiple reward functions, latent variables, or probabilistic models to capture the uncertainty and diversity of the rewards.

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Dr. Mario Javier Pérez Rivas

Director of AI and Cloud Infrastructure Services
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In the realm of multi-objective reinforcement learning (RL), the robot chef scenario exemplifies the complexity of creating advanced reward systems. This robot must craft meals that are delicious, healthy, and cost-effective, demanding a multifaceted reward structure. It requires a balance between health, cost, and culinary creativity, with an emphasis on understanding subjective tastes. The approach involves training models for different cooking styles and dynamically adapting to changing preferences and market conditions. This case underscores the broader RL challenge of devising systems adept at handling intricate, multi-dimensional tasks.

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3 Multi-objective optimization

Once the reward function is defined and estimated, the next step in RL is to optimize the policy, which specifies how the agent should act in different situations. A common approach is to use a single-objective optimization method, such as value iteration or policy gradient, which maximizes the expected scalar reward. However, this may not reflect the true preferences or trade-offs of the agent, and may ignore the Pareto front, which is the set of optimal policies that cannot be improved on one objective without worsening another. To address this challenge, some methods use multi-objective optimization methods, such as scalarization, decomposition, or evolutionary algorithms, which aim to find or approximate the Pareto front.

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Dr. Mario Javier Pérez Rivas

Director of AI and Cloud Infrastructure Services
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In multi-objective optimization for reinforcement learning, the focus is on balancing conflicting objectives to find optimal policies (Pareto front). Techniques like scalarization simplify multiple objectives into one, while decomposition segments the problem into neural-network-modeled parts. Advanced methods like Pareto-front-based deep reinforcement learning enhance optimization efficiency. Hypernetworks are used to learn the entire Pareto front for effective post-training selection. These approaches are key in managing simultaneous objectives in real-world scenarios. My go-to tool as a machine learning consultant is Pymoo, offering a variety of algorithms and visualization tools for multi-objective optimization challenges.

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4 Policy selection and evaluation

The final step in RL is to select and evaluate the policy, which determines how the agent performs and behaves in the environment. A common approach is to use a single criterion, such as the expected scalar reward, the regret, or the robustness, which measures how well the policy meets the objectives. However, this may not capture the full picture of the policy, and may overlook the trade-offs, uncertainties, or conflicts among the objectives. To address this challenge, some methods use multiple criteria, such as hypervolume, diversity, or satisfaction, which measure how well the policy covers the Pareto front, exploits the different objectives, or satisfies the preferences of the agent.

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Dr. Mario Javier Pérez Rivas

Director of AI and Cloud Infrastructure Services
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While multi-objective approaches offer a valuable lens, policy selection and evaluation in RL are inherently complex. Beyond multiple objectives, real-world scenarios often involve: Uncertainties: Incomplete information, dynamic environments, and inherent stochasticity necessitate methods that consider these factors. Problem-specific characteristics: Different problems demand tailored approaches, considering the number of objectives, their interplay, and the agent's capabilities. Therefore, a holistic view requires acknowledging the multi-objective framework's strengths while recognizing the need for flexibility and adaptation based on the specific problem.

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5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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Arta Asadi

Machine Learning Engineer@ Smart Land Solutions
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Remember reward shaping is an engineering id does need deep understanding of the dynamics of the system, try to learn the problem and system first!

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How do you deal with multi-objective or conflicting rewards in RL?

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1 Reward function design

2 Reward function estimation

3 Multi-objective optimization

4 Policy selection and evaluation

5 Here’s what else to consider

Reinforcement Learning

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