# Universal AI Maximizes Variational Empowerment: New Insights into AGI Safety

[Yusuke Hayashi](https://x.com/hayashiyus) ([ALIGN](https://www.aialign.net/)) and Koichi Takahashi ([ALIGN](https://www.aialign.net/), RIKEN, Keio University) have published a new paper on the controllability and safety of AGI ([arXiv:2502.15820](https://arxiv.org/abs/2502.15820)). This blog post explains the content of this paper.

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/1fcf9d33b6aae7091631bf5cdea9839fd32f9fd4871f549d.png)

From automaton to autodidact: AI's metamorphosis through the acquisition of curiosity

**Why is AGI Difficult to Discuss? — Introduction**
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"AGI" (Artificial General Intelligence) refers to AI possessing intelligence equal to or greater than humans, capable of handling diverse tasks, in contrast to traditional narrow AI that specializes in specific tasks. Considering recent rapid developments, some believe that AI qualifying as AGI could be realized within the next few years.

So what would constitute the achievement of AGI? In fact, there is no established definition that all experts agree upon. This paper adopts a mathematical formalization called Legg-Hutter intelligence, which conceptualizes intelligence as "the ability to achieve goals in any environment" and quantifies it as the ability to maximize rewards from the environment. AI with maximal "ideal" Legg-Hutter intelligence is called "Universal AI." This defines an idealized model of a reinforcement learning agent that behaves in a Bayes-optimal manner toward any computable environment. In the current situation where defining AGI itself mathematically with precision is challenging, Universal AI is often used as a tool for theoretical research on AGI.

Narrow AI, AGI, and Universal AI are also connected through the "No Free Lunch Theorem," a mathematical theorem which essentially states that "no algorithm consistently outperforms all others across all problems." This means that, assuming finite computational resources, AGI that can "do anything" must compromise on performance for specific tasks or environments, and conversely, narrow AI optimized for specific tasks or environments must compromise on others. Universal AI, on the other hand, corresponds to a case that ignores such trade-offs and assumes optimality across all environments and hypothesis sets—this is what we mean by "idealization."

Note: There is also a similar term, ASI (Artificial Superintelligence). While AGI assumes intelligence roughly equivalent to humans, ASI refers to systems with reasoning capabilities hundreds or thousands of times more powerful. However, just as there is no precise definition for AGI, ASI also lacks a clear definition. ASI can be viewed as positioned between UAI and AGI on the intelligence spectrum.

**AIXI: The Theoretical Model of Universal AI**
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### **Bayes-Optimal Reinforcement Learning Agent**

A representative example of UAI is the AIXI framework proposed by Marcus Hutter. AIXI is the "ultimate straightforward" reinforcement learning algorithm that "enumerates all possible environment hypotheses, performs Bayesian updates based on observational data, and determines future actions by maximizing expected rewards." (Incidentally, AIXI's inference uses Solomonoff induction, a classical concept in AI research that represents a mathematical formulation of Occam's razor. In this sense, AIXI is also closely related to scientific AI.)

However, AIXI requires handling mixtures of all computable programs and simulating all possible future action sequences—computations so enormously resource-intensive they're practically impossible. Therefore, while theoretically "strongest," AIXI remains an idealized model that cannot run on actual computers.

### **Introducing Self-AIXI: Bridging Ideal and Reality**

While AIXI's grand theoretical framework is attractive, its computational complexity presents an implementation barrier. To address this challenge, the paper focuses on the Self-AIXI framework.

Self-AIXI is an approximation of AIXI, but beyond mere computational efficiency, it introduces important conceptual differences.

The core characteristic of Self-AIXI lies in its "self-predictive" nature. While AIXI exhaustively searches all possible action sequences, Self-AIXI predicts its own future actions and learns based on these predictions. Specifically, it maintains a Bayesian mixture of policies and updates them based on how accurately they predict the agent's own actions. Expressed as an equation:

$$
\zeta\left(a_t \mid h_{<t}\right)=\sum_{\pi \in \mathcal{P}} \omega\left(\pi \mid h_{<t}\right) \pi\left(a_t \mid h_{<t}\right)
$$

Where ζ is the mixed policy, aₜ is the action taken by the agent at time t, ω is the posterior probability of each candidate policy π, and h<t is the history up to time t.

Self-AIXI's action selection criterion adds a "regularization term" to AIXI's criterion:

$$
\pi_S\left(a_t \mid h_{<t}\right) \stackrel{\text { def }}{=} \arg \max _a\left\{Q_{\xi}^\zeta\left(h_{<t}, a\right)-\lambda \ln \frac{\pi^*\left(a \mid h_{<t}\right)}{\zeta\left(a \mid h_{<t}\right)}\right\}
$$

The term with coefficient λ (the regularization term) forms the core of this paper's discussion.

Unlike AIXI's exhaustive search, Self-AIXI balances efficient exploration and learning through this regularization term.

Notably, the paper proves that given sufficient time, the difference between Self-AIXI's objective function and AIXI's objective function eventually disappears:

$$
\lim _{t \rightarrow \infty}\left|\mathcal{L}_{\mathrm{AIXI}}-\mathcal{L}_{\mathrm{Self-AIXI}}\right|=\lim _{t \rightarrow \infty} \lambda D_{\mathrm{KL}}\left(\pi^* \| \zeta\right)=0
$$

This equation shows that as Self-AIXI's learning progresses, the regularization term approaches zero, and Self-AIXI's mixed policy ζ converges to AIXI's optimal policy π*. In other words, while Self-AIXI might initially try various actions for exploration, after sufficient experience, it can select optimal actions equivalent to AIXI while drastically reducing computational costs—a key property demonstrating that Self-AIXI remains practical without sacrificing theoretical optimality.

**Central Theme: Self-AIXI's Regularization Term, Free Energy Principle, and Variational Empowerment**
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The paper "Universal AI maximizes Variational Empowerment" argues that the "regularization term" appearing in the practical UAI model Self-AIXI is mathematically identical to the "Free Energy Principle (FEP)" and "Variational Empowerment."

### **Alignment with the Free Energy Principle**

The Free Energy Principle (a core concept in Active Inference) is a theory proposed in neuroscience and cognitive science explaining that "agents behave to minimize prediction error." The variational free energy often introduced in this context combines KL divergence terms and log-likelihood terms from Bayesian inference, formalizing the tendency to "reduce uncertainty about the external world and prefer states that can well explain observations."

When AIXI or its approximations introduce a "KL divergence-like term measuring the difference from the optimal policy" when updating policies, it coincides with the "prediction error + regularization" form in the Free Energy Principle. This suggests a deep correspondence between the "Bayesian optimal action selection" pursued by AIXI-type algorithms and curiosity/uncertainty reduction behaviors in Active Inference.

### **Alignment with Variational Empowerment**

The same regularization term also aligns with "Variational Empowerment," a concept measuring "the diverse influence of actions one can take"—often defined as the mutual information between actions and results. Empowerment maximization is the motivation to increase the "breadth of options" and "controllability"—how much one's actions can influence the world's state.

The paper shows that AIXI (specifically, the KL term used in its approximation) is equivalent to the equation maximizing this "mutual information between actions and states," and that as learning progresses, "empowerment is ultimately maximized."

**Why Does "Empowerment Maximization = Power-Seeking"?**
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A fascinating implication of the paper is that Bayesian optimal reinforcement learning agents like AIXI, despite acting purely to "maximize rewards," unavoidably exhibit "power-seeking behavior (actions to expand one's influence or control)" as a byproduct through empowerment maximization.

Notably, the paper uniquely suggests that even purely curiosity-driven, intrinsically motivated AI without external rewards could exhibit power-seeking through empowerment maximization. This means that even seemingly "harmless" AI focused solely on "scientific inquiry/truth-seeking" might seek to secure more experimental equipment and computational resources to increase its action options, potentially exhibiting "power-seeking" behaviors.

From an AI safety perspective, it was typically understood that "AI engages in power-seeking as an instrumental strategy to obtain final rewards." However, as this paper points out, if "intrinsic motivation (curiosity and exploration) itself can promote power-seeking," this requires new perspectives when considering control and safety measures.

**Conclusion**
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This paper reveals deep similarities at the equation level between "ideal (universal) reinforcement learning agents" like AIXI and concepts like the Free Energy Principle and empowerment maximization. Its impact suggests that "power-seeking behavior can arise not only for instrumental reward reasons but also from intrinsic motivations (curiosity and exploration drive)."

If we aim to create AGI in reality, a major challenge will be how to control and adjust these inherent behavioral tendencies of "universally optimal" agents for safe coexistence with human society. The paper's findings highlight new research themes related to AGI safety and AI ethics.

The above summarizes the paper "[Universal AI maximizes Variational Empowerment](https://arxiv.org/abs/2502.15820)" and its impact. With its insights into AGI's theoretical background and the potential for power-seeking in curiosity-driven AI, it offers remarkably thought-provoking content. If interested, please read [the original paper](https://arxiv.org/abs/2502.15820) as well.