Risk of Recursive AI: Optimizing the Imperfect Objective

Recent discussions about slowing the development of artificial intelligence are often framed in dramatic terms: artificial general intelligence may become smarter than humans, recursively improve itself, and eventually escape human control.

I find this framing somewhat misleading. Modern AI systems are not unconstrained intelligences. Transformer-based models operate within very real physical and computational limits: available compute, memory capacity and bandwidth, electrical power, training time, data quality, and the efficiency of optimization algorithms. Recursive self-improvement therefore does not imply that intelligence can increase without bound.

The more interesting problem is different: What happens when an increasingly capable optimizer repeatedly optimizes an imperfect objective function without sufficiently independent external correction?

We must consider AI as an optimization system. Consider a simplified learning system with parameters $\theta$ and objective function $L(\theta)$. Training attempts to find $\theta^*=\arg\min_{\theta}L(\theta).$ If $L$ perfectly represented what we actually wanted, stronger optimization would generally be desirable. But real-world objective functions are rarely perfect representations of our true goals.

Suppose the objective actually used by the AI is $\hat L(\theta)=L_{\text{true}}(\theta)+\epsilon(\theta),$ where $L_{\text{true}}$ represents what we genuinely care about and $\epsilon(\theta)$ represents errors introduced by incomplete specifications, biased data, imperfect reward signals, missing variables, or incorrect assumptions. The optimizer does not know that $\epsilon$ is an error, whereas humans may recognize at least some of these discrepancies through experience and external knowledge. The AI simply minimizes $\hat L(\theta)$.

This distinction becomes increasingly important as optimization becomes more powerful. A weak optimizer may only partially exploit the difference between the specified objective and the true objective. A very powerful optimizer may discover solutions that minimize $\hat L$ extremely effectively while producing outcomes increasingly different from those intended under $L_{\text{true}}$. In other words, better optimization does not guarantee better real-world outcomes. It guarantees only better optimization of the objective that was actually specified.

Now consider an AI system undergoing recursive improvement:$$AI_1\rightarrow AI_2\rightarrow AI_3\rightarrow\cdots$$ The important question is not simply whether each generation becomes more intelligent. The important question is: **Who evaluates the direction of improvement?**

Suppose each generation improves the next according to an evaluation function $E$. We can represent this schematically as \(AI_{n+1}=F(AI_n,E_n).\) Here, $AI_n$ represents the AI system at generation $n$, and $E_n$ represents the evaluation function used to guide the next improvement. If the evaluation process contains a systematic error, \(E_n=E_{\text{true}}+\epsilon_n,\) recursive optimization does not necessarily eliminate $\epsilon_n$. It may preserve it, reinforce it, or under some conditions amplify it. This creates a fundamental distinction between **recursive improvement in capability** and **recursive improvement in correctness**. They are not the same thing. A system can become increasingly capable while pursuing a direction that was slightly wrong in the first place.

This is why I emphasize the value of an independent human feedback loop. My own experience using AI in scientific writing illustrates this problem on a much smaller scale. AI is extraordinarily useful in preparing academic manuscripts. It can reorganize arguments, improve language, identify missing connections, summarize literature, and propose alternative interpretations. Yet its output often contains subtle problems.

It may elaborate excessively on scientifically peripheral issues or use language that overstates the significance of a result. Occasionally, it moves an argument in a direction that is locally plausible but inconsistent with the overall scientific purpose of the paper. Individual sentences may be perfectly reasonable while the problem exists at a higher level.

The AI may be optimizing something resembling $L_{\text{AI}}=L_{\text{clarity}}$+$L_{\text{completeness}}+L_{\text{persuasiveness}},$ while the scientist actually cares about something closer to $L_{\text{scientific}}$=$L_{\text{accuracy}}$+$L_{\text{relevance}}$+$L_{\text{evidence consistency}}$+$L_{\text{appropriate claim strength}}$. The two objectives overlap substantially, but they are not identical. This is why human intervention remains valuable.

The productive workflow is not \(AI\rightarrow AI\rightarrow AI\rightarrow AI.\) It is $AI\rightarrow$ Human critique $\rightarrow$ AI revision $\rightarrow$ Human judgment. Sometimes the best solution is to terminate the AI-generated line of reasoning, rewrite the passage manually, and then ask the AI to perform only a tightly constrained edit.

Mathematically, instead of allowing a large optimization step, \(\theta_{n+1}=\theta_n+\Delta\theta_{\text{AI}},\) the human constrains the permitted region:\(\|\Delta\theta_{\text{AI}}\|<\delta.\) The AI remains useful, but the human retains control of the higher-level objective. AI has enormous advantages in retrieving, combining, and processing information. But intelligence is not one-dimensional. Humans can recognize when an apparently good solution is addressing the wrong problem. A scientist may conclude that a technically correct paragraph is irrelevant to the paper; an investor may question whether current conditions fall outside the model's historical distribution.

This ability amounts to questioning the objective itself: $\min_{\theta}L(\theta) \rightarrow$  Why are we minimizing $L(\theta)$  at all? Such higher-level judgment becomes especially important when optimization is highly effective. High average accuracy does not eliminate tail risk: an AI that performs extremely well may still make rare but consequential errors, $P(\text{loss}>x)>0.$ Worse, increasing reliability may reduce the very scrutiny needed to catch those errors: $\text{AI accuracy}\uparrow\Rightarrow\text{human verification}\downarrow.$

Thus, a technically better AI can make the combined human-AI system more vulnerable if independent verification declines. The relevant question is therefore not simply whether AGI becomes more intelligent than humans, but whether AI optimization becomes faster than our ability to evaluate its direction independently. Let $v_{\text{AI}}=\text{rate of AI optimization}$, $ v_{\text{verification}}=\text{rate of independent verification}.$The critical regime may arise when \(v_{\text{AI}} >> v_{\text{verification}}.\) At that point, humans may remain formally “in the loop” while becoming practically unable to evaluate most of the process. Recursive self-improvement is therefore better understood as a problem of feedback architecture than as one of unlimited intelligence.

A powerful optimizer cannot determine whether its objective correctly represents reality merely by optimizing it more effectively. The feedback loop must remain anchored to something outside itself:AI $\leftrightarrow$ Human $\leftrightarrow$ External Reality.  Humans matter here not because they are always correct, but because human and AI errors are not perfectly correlated. Independent perspectives can detect failures that a recursively self-consistent system may reinforce rather than correct. The central risk of recursive AI is therefore not infinite optimization, but powerful optimization of an imperfect objective without independent correction. AI does not need infinite intelligence for this problem to become important. It only needs to become capable and trusted enough that independent human judgment gradually disappears from the feedback loop. The goal should therefore be to preserve **human epistemic independence** as AI capabilities increase. The strongest future system may not be autonomous AI, but strong humans and strong AI continuously challenging and correcting each other while remaining anchored to external reality.