Agentic AI Optimisation

• Agentic AI Optimisation is a paradigm that recasts optimization tasks as agent–environment interactions, integrating adaptive decision-making with resource-awareness.
• It leverages minimal state representations and discrete action sets with reinforcement learning to dynamically select update strategies under resource constraints.
• Empirical results show AAIO outperforms static optimizers in various applications, from deep network training to online control systems.

Agentic AI Optimisation (AAIO) designates a paradigm within artificial intelligence whereby optimization procedures, decision-making, and operational execution are recast as agent–environment interactions, enabling the dynamic, autonomous selection of strategies or actions. AAIO leverages agentic architectures—typically composed of AI agents that perceive the state of an environment, select among diverse algorithmic or tooling options, and iteratively update their policies—often using reinforcement learning (RL) or other adaptive feedback mechanisms. Notably, AAIO distinguishes itself from static optimization by embedding computational rationality, resource-awareness, and strategic adaptation into the optimization process itself, leading to robust performance especially under real-world constraints such as limited computational budgets.

1. Primitive State Representations and Sequential Decision Frameworks

In AAIO, traditional iterative optimization steps are abstracted as a sequence of agent–environment interactions, allowing the “agent” to select among a set of primitive update rules according to succinct, low-dimensional state encodings (Sala, 7 Jun 2024). This state representation avoids tracking the full optimization history and instead condenses progress and resource use into discrete features, for example:

• The normalized, discretized value of the current objective function:

$$s_{k+1}^1 = \left\lfloor \min\left(1, \max\left(0, \frac{y_{k+1} - l}{u - l}\right)\right) \cdot (m_1 - 1) \right\rfloor + 1$$

• The discretized measure of computational budget used:

$$s_{k+1}^2 = \left\lfloor \frac{k}{K/m_2} \right\rfloor + 1$$

forming a state tuple $s_{k+1} = (s_{k+1}^1, s_{k+1}^2)$.

This primitive abstraction enables the agent to generalize across problem instances by ignoring fine-grained details and focusing on actionable context, making the RL problem tractable even when the underlying optimization task is complex.

2. Agent–Environment Interaction and RL-Based Update Selection

AAIO reconceptualizes optimization as an RL problem. At each iteration $k$, the environment supplies a current state $s_k$ and possible actions (update rules or strategies). The agent chooses an action $a_k$ from a discrete set of update policies $$\mathcal{H} = \{(H_1, \theta_1), \ldots, (H_J, \theta_J)\}$$, where each $H_j$ encodes a candidate optimizer with its parameters. The action is applied as:

$$x_{k+1} = H_{a_k}(x_k, f(x_k), \nabla f(x_k), \theta_{a_k})$$

The environment responds with a new objective, next state, and a scalar reward, closing the iteration loop. Through this mechanism, classical and heuristic update steps are subsumed as environment-driven actions, enabling dynamic adaptation and explicit allocation of the “computational budget” in resource-constrained settings.

The agent's policy $\pi$ is trained (e.g., via SARSA with $\epsilon$-greedy exploration) to maximize the expected cumulative improvement, using a Q-table or value function approximator, updated as:

$$Q(s_k, a_k) \leftarrow (1-\alpha) Q(s_k, a_k) + \alpha \left[r_{k+1} + \gamma Q(s_{k+1}, a_{k+1})\right]$$

where $\alpha$ is the learning rate and $\gamma$ the discount factor.

3. Empirical Performance and Comparison to Monolithic Optimizers

The AAIO approach has been empirically validated on quadratic optimization benchmarks of the form:

$$f(x) = \frac{1}{2} x^\top A x - b^\top x + c, \quad \text{with } A \succ 0$$

Standard algorithms, such as Nesterov Accelerated Gradient (NAG) tuned with optimal hyperparameters, provide a fixed strategy with theoretical convergence guarantees. However, in fixed-budget settings, superior real-world performance may be obtained by dynamically adjusting strategy in response to early-stage progress and resource utilization.

Experimental deployments demonstrate that AAIO-trained policies outperform conventional optimizers in terms of final objective value and wall-clock runtime under constrained computational budgets. By exploiting local context, the agent adapts between aggressive and conservative update rules, effectively employing warm-start or multi-phase strategies that are difficult to encode in static schemes (Sala, 7 Jun 2024).

4. Complexity Management via Elementary RL and Action Abstraction

AAIO leverages simple RL algorithms combined with minimalistic state representations to alleviate the curse of dimensionality. This pragmatic reduction enables:

• Simplicity: The agent is not overwhelmed by unnecessary details, facilitating efficient learning.
• Flexibility: Multiple traditional update rules and parameterizations are available, enabling hybridized or context-sensitive strategies.
• Robustness: The policy, when trained on a spectrum of problem instances, can generalize and tune itself in situations where single-algorithm hyperparameter optimization may fail due to overfitting or model mismatch.

This yields agentic optimizers that are both lightweight and adaptive, providing a practical route to scalable RL-based optimization in real systems.

5. Broader Applications, Implications, and Future Prospects

AAIO's paradigm extends beyond conventional mathematical programming and can be adopted across domains where iterative improvement under resource constraints is required. Examples include:

• Large-scale deep neural network training, where dynamic adaptation of optimizer settings becomes crucial as training phases progress.
• Online control systems, where rapid adaptation is essential in non-stationary environments.
• Adaptive scientific or engineering design, where resource-aware exploration and exploitation strategies must co-exist.

By embedding computational rationality—explicit attention to progress, resource allocation, and adaptation—into the update loop, AAIO provides a blueprint for managing complexity in large-scale, real-world optimization problems.

Conceivably, such approaches can be expanded using more sophisticated agents, richer state representations (e.g., multi-modal signals, histories), and hierarchical decision-making, thus paving the way for next-generation, agent-driven optimization frameworks that remain transparent, interpretable, and computationally efficient.

6. Limitations and Modeling Considerations

While AAIO demonstrates strong empirical results under the tested scenarios:

• The approach depends on careful discretization and meaningful state abstraction; an ill-chosen state space may limit learning and generalization.
• Scalability to high-dimensional or highly non-convex problems may require richer function approximation or hierarchical policy structures.
• The action set must be engineered to capture effective update strategies for the target domain; unused or redundant strategies can increase learning noise.
• The choice of reward shaping, exploration rate (ε), and learning rate (α) all influence convergence and effectiveness.

Given these constraints, implementations must tailor state, action, and reward designs to application-specific requirements, supporting the extension of AAIO concepts to broader classes of optimization tasks.

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AAIO constitutes a methodologically rigorous, practically motivated approach to optimization, reconciling RL-based policy learning with classic algorithmic strategies and resource-aware adaptation. It is positioned as a cornerstone for future research and application in agentic, adaptive optimization across computational and engineering domains (Sala, 7 Jun 2024).