1. Research agenda for training aligned AIs using concave utility functions following the principles of homeostasis and diminishing returns
By Roland Pihlakas
This conceptual overview post is intended to explain what I mean by the principles of "homeostasis", "diminishing returns", and "balancing" - how these ideas differ, complement, and interact with each other. Alongside, there is also an overview of our research agenda.
What am I trying to promote, in simple words:
I want to build and promote AI systems that are trained to understand and follow two fundamental principles from biology and economics:
Moderation - Enables the agents to understand the concept of “enough” versus “too much”. The agents would understand that too much of a good thing would be harmful even for the very objective that was maximised for, and they would actively avoid such situations. This is based on the biological principle of homeostasis and addresses mainly bounded ultimate objectives. Active avoidance of “too much” is a significantly stricter principle than the more widely known partially overlapping idea of “mild optimisation”.
Balancing - Enables the agents to keep many important objectives in balance, in such a manner that having average results in all objectives is preferred to extremes in a few. This addresses mainly the economic principle of diminishing returns in unbounded instrumental objectives, but also applies to homeostasis.
Figure 1 and 2: Both utility functions are concave, though in different ways:
2. Why modelling multi-objective homeostasis is essential for AI alignment (and how it helps with AI safety as well)
By Roland Pihlakas
Much of AI safety discussion revolves around the potential dangers posed by goal-driven artificial agents. In many of these discussions, the agent is assumed to maximise some utility metric over an unbounded timeframe. This simplification, while mathematically convenient, can yield pathological outcomes. A classic example is the so-called “paperclip maximiser”, a “utility monster” which steamrolls over other objectives to pursue a single goal (e.g. creating as many paperclips as possible) indefinitely. “Specification gaming”, Goodhart’s law, and even “instrumental convergence” are also closely related phenomena.
However, in nature, organisms do not typically behave like pure maximisers. Instead, they operate under homeostasis: a principle of maintaining various internal and external variables (e.g. temperature, hunger, social interactions) within certain "good enough" ranges. Going far beyond those ranges — too hot, too hungry, too socially isolated — leads to dire consequences, so an organism continually balances multiple needs. Crucially, "too much of a good thing" is just as dangerous as too little.
This post argues that an explicitly homeostatic, multi-objective model is a more suitable paradigm for AI alignment. Moreover, correctly modelling homeostasis increases AI safety, because homeostatic goals are bounded — there is an optimal zone rather than an unbounded improvement path. This bounding lowers the stakes of each objective and reduces the incentive for extreme (and potentially destructive) behaviours.
Homeostasis — the idea of multiple objectives each with a bounded “sweet spot” — offers a more natural and safer alternative to unbounded utility maximisation. By ensuring that an AI’s needs or goals are multi-objective and conjunctive, and that each is bounded, we significantly reduce the incentives for runaway or berserk behaviours.
Such an agent tries to stay in a "golden middle way", switching focus among its objectives according to whichever is most pressing. It avoids extremes in any single dimension because going too far throws off the equilibrium in the others. This balancing act also makes it more corrigible, more interruptible, and ultimately safer.
There are two distinct types of balancing involved:
1. Balancing of a single homeostatic objective - keeping the actual value not too low, not too high.
2. Balancing across objectives.
In short, modelling multi-objective homeostasis is a step toward creating AI systems that exhibit the sane, moderate behaviours of living organisms — an important element in ensuring alignment with human values. While no single design framework can solve all challenges of AI safety, shifting from “maximise forever” to “maintain a healthy equilibrium” is a crucial part of the solution space.
3. Concave vs convex utility functions in the negative domain - Balancing and Risk Aversion versus Strategic Selectiveness and Prospect Theory
By Roland Pihlakas
Economic theories often focus on the “gains” side of utility and how our multi-objective preferences are balanced there. A well known formulation is to use diminishing returns - a concave utility function, which mathematically results in a balancing action where an individual prefers averages in all objectives to extremes in a few objectives.
But, what happens in the negative domain of utility? How do humans handle risks and losses? Turns out, it might be not so simple as with gains.
One might imagine that one could apply a concave utility function to the negative domain as well, in order to balance the individual losses, or to equalise and provide an equal treatment in case of multiple individuals. This would resonate with the idea that generally people prefer averages in all objectives to extremes in a few objectives. As an example, a negative exponential utility function would achieve that.
Yet there is a well known theory named “Prospect theory”, which claims instead that our preferences in the negative domain are convex.
As I see it, this contradiction between the theories of “preferring averages over extremes” and “the Prospect Theory” may be underexplored, especially with regards to how it is relevant to AI safety.
I could see the benefit of the Prospect Theory’s approach as well - for example when pursuing two rabbits, then I would not want to balance my distance from both. Instead I would choose the nearest rabbit and accept the loss of the other rabbit.
At the same time, there are many practical life situations, where we indeed want to distribute our investments or bets and risks in order to be more robust, to diversify our options, or to sustain a maximally balanced level of essential resources, even if they are at a lesser than desired level. For example, if we are poor in both water and food resources, we would not trade all remaining available water for more food, or all remaining available food for more water. In economics such objectives are called complementary goods - both goods are necessary.
I suspect that both theories have their scope where they are most appropriate. It would be helpful to explore and define more precisely what is the scope of appropriate application of both theories, and how should an AI agent switch between these contradictory approaches to risks and losses.
This discrepancy raises an important question: How should AI agents handle risks and losses to align with human expectations? If an AI agent consistently applies multi-objective balancing strategies in all scenarios, it might become overly cautious, potentially missing out on beneficial opportunities, or paradoxically causing even more harm by trying to achieve unrealistic compositions of multiple objectives - especially when trying to recover losses in an impossible or very difficult objective, which would result in bringing down everything else. Conversely, if it easily gives up on any difficulty and accepts risks or losses in the remaining objectives while choosing to focus only on gains in one or few easiest objectives, it might make dangerously reckless decisions, and become exploitative (since caring about others is too difficult), an unbounded maximiser, essentially losing its multi-objective balanced nature.