Model Advisor Agent Framework

• Model Advisor Agent is a modular reinforcement learning framework that decomposes complex tasks into specialized advisor components.
• It employs diverse planning methods—egocentric, agnostic, and empathic—to aggregate local Q-values and optimize global decision-making.
• The approach enhances scalability, robustness, and efficiency in multi-objective systems by harmonizing independent, specialized contributions.

A Model Advisor Agent is an architectural and algorithmic concept in which tasks—most notably in reinforcement learning and related agent-based systems—are modularly decomposed, with advice or recommendations synthesized by a set of specialized advisor components. These advisors may be instantiated as independent learners, policy components, or sub-models, and their outputs are aggregated through formal mechanisms to inform or steer a global controller or decision-maker. This paradigm addresses complex challenges such as coordination, conflicting objectives, robustness to sub-optimal advice, and more efficient learning, and has broad implications for both theoretical advances and practical real-world systems.

1. Modular Decomposition and Advisor Framework

In the Multi-Advisor Reinforcement Learning (MARL) framework (Laroche et al., 2017), a single-agent reinforcement learning problem is distributed across $n$ learners—termed advisors. Each advisor targets a specific subfacet of the overall task, such as a particular goal or constraint (e.g., collecting a specific object, avoiding hazards). Each advisor operates over a (possibly reduced) local state space and a specialized reward structure, often with the global reward linearly decomposed:

$R(x, a) = \sum_j w_j R_j(x_j, a)$

where $w_j$ are advisor-specific weights and $x_j$ are local state representations.

The core design pattern is an explicit advisor-aggregator interface:

• Advisors compute local Q-values $Q_j(x_j, a)$.
• These Q-values are communicated to an aggregator which synthesizes a global value via a linear summation:

$Q_\Sigma(x, a) = \sum_j w_j Q_j(x_j, a)$

• The aggregator selects the final action via a policy such as $f_\Sigma(x) = \arg \max_a Q_\Sigma(x, a)$.

This distributed structure allows specialized reasoning and reduces complexity per advisor, while the aggregator coordinates and integrates advice for overall task fulfillment.

2. Local Planning Algorithms and Aggregation Strategies

Advisor agents rely on local planning policies. Three principal paradigms are systematically compared:

• Egocentric Planning: Each advisor optimizes for its own outcome, updating values as

$$Q_j^\text{ego}(x_j, a) = \mathbb{E}[r_j + \gamma \max_{a'} Q_j^\text{ego}(x'_j, a')]$$

After aggregation ($Q_\Sigma^\text{ego}$), a max–sum inversion occurs, leading to overestimation when advisors disagree—manifesting in attractor states that the system cannot reliably escape.

• Agnostic Planning: Advisors assume future actions are uniformly random, leading to

$$Q_j^\text{agn}(x_j, a) = \mathbb{E}[r_j + \frac{\gamma}{|A|} \sum_{a'} Q_j^\text{agn}(x'_j, a')]$$

Aggregating agnostic Q-values avoids overestimation but unduly penalizes rare negative events, resulting in risk-averse, inefficient behaviors around critical states.

• Empathic Planning: Advisors bootstrap on the aggregator's predicted action, solving

$$Q_j^{ap}(x_j, a) = \mathbb{E}[r_j + \gamma Q_j^{ap}(x'_j, f_\Sigma(x'))]$$

This coupling aligns local updates with the actual policy executed, theoretically recovering global optimality when advisors have access to the full global state. It avoids both the overestimation (attractor) and excessive caution problems.

The choice of planning paradigm directly impacts learning performance, convergence, and solution quality. The empathic formulation, in particular, is shown to provide robust, near-optimal solutions while maintaining modular decomposition.

3. Mathematical Characterization and Attractor Pathologies

Precise mathematical characterization underpins the advisor agent framework:

• Aggregated Value Function:

$Q_\Sigma(x, a) = \sum_j w_j Q_j(x_j, a)$

• Egocentric Attractor Formalization:

A state $x$ is an attractor if

$$\max_a \sum_j w_j Q_j^\text{ego}(x_j, a) < \gamma \sum_j w_j \max_a Q_j^\text{ego}(x_j, a)$$

This inequality captures the core issue: separation between local maxima and the global action preferred by the sum—resulting in preference to remain in $x$ even if it is suboptimal from a holistic perspective.

• Empathic Global Consistency:

Empathic planning ensures that, if advisors see the full state,

$$Q_\Sigma^{ap}(x, a) = \mathbb{E}[r + \gamma Q_\Sigma^{ap}(x', f_\Sigma(x'))]$$

matching the standard global Bellman optimality equation.

These formulations provide criteria for method selection, parameter tuning (e.g., discount factor $\gamma$), and diagnosis of convergence issues in both experimental and real-world settings.

4. Empirical Evaluation and Practical Behavior

Empirical validation using a fruit collection task in the Pac‐Boy domain illustrates the effects of each planning method:

• Egocentric planning with low $\gamma$ avoids attractors and achieves near-optimal policies. As $\gamma$ increases, attractor pathologies become severe—the agent “waits”, failing to make progress toward multi-goal fulfillment.
• Agnostic planning proves robust to attractors but overly penalizes risk, leading to slow or failed task completion near states with rare but catastrophic negative outcomes.
• Empathic planning performs at or near low-$\gamma$ egocentric levels across discount factors and demonstrates greater robustness in the presence of reward noise and partial observations.

Quantitative learning curves in controlled experiments reaffirm that planner choice is critical, and the empathic scheme demonstrates strong resilience and policy quality.

5. Design Implications for Advisor Agent Systems

The paradigm of modular advisor agents has several key implications for multi-objective and multi-constraint decision-making systems:

• Decomposition enables scalability: Each advisor is only responsible for a subset of the problem, allowing simple state representations and tractable learning updates.
• Planning method selection is non-trivial: Naïve local optimization (egocentric) or risk-agnostic averaging (agnostic) can result in behavior that is suboptimal or even unstable when advisors' goals conflict.
• Empathic planning achieves synchronization: By explicitly aligning advisor bootstrapping with the aggregator’s expected action, system-level coherence is achieved without loss of modularity.
• Parameterization (γ, advisor reward design) matters: Theoretical and practical guidance is provided to avoid attractors (e.g., maintain appropriately low discount factors; construct reward functions that incentivize progress).
• Robustness to information incompleteness: While full-state access yields optimality guarantees, empathic planning remains resilient even when advisors operate over partial observability.

This approach has direct relevance for the construction of advisor agents in RL and AI–augmented planning systems, with applications from multi-objective robotics to hierarchical decision-making in complex software systems.

6. Broad Applicability and Theoretical Significance

The multi-advisor agent framework forms a basis for designing complex, modular AI systems in which expert modules contribute specialized knowledge to a central decision process. Its mathematical rigor enables formal analysis of pathological behaviors, guides architecture choices, and supports practical deployment.

By demonstrating how localized expertise can be robustly and optimally aggregated (most effectively via empathic mechanisms), this research establishes a foundation for agent-based architectures that are both scalable and theoretically grounded. It directly informs subsequent works that extend from single-agent to multi-agent or hierarchical RL, and provides a mechanism for overcoming the limitations of overcommitment to any single specialized objective.

Empirical confirmation across varied scenarios supports claims of improved learning speed, policy robustness, and overall system effectiveness, especially when balancing conflicting subgoals or navigating ambiguous regions of the state space.

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In summary, the Model Advisor Agent paradigm—originating in the Multi-Advisor RL framework—provides a modular, mathematically principled approach for decomposing and solving complex sequential decision problems via coordinated advisor components and aggregation mechanisms. The selection of local planning methods, particularly the empathic scheme, is central to achieving optimal, stable, and robust global behavior, and the architecture informs the design of scalable and efficient intelligent systems across diverse domains (Laroche et al., 2017).