Sequence Summary. This sequence documents research by SatisfIA, an ongoing project on non-maximizing, aspiration-based designs for AI agents that fulfill goals specified by constraints ("aspirations") rather than maximizing an objective function​​. We aim to contribute to AI safety by exploring design approaches and their software implementations that we believe might be promising but neglected or novel. Our approach is roughly related to but largely complementary to concepts like quantilization and satisficing (sometimes called "soft-optimization"), Decision Transformers, and Active Inference.

This post describes the purpose of the sequence, motivates the research, describes the project status, our working hypotheses and theoretical framework, and has a short glossary of terms. It does not contain results and can safely be skipped if you want to get directly into the actual research.

Epistemic status: We're still in the exploratory phase, and while the project has yielded some preliminary insights, we don't have any clear conclusions at this point. Our team holds a wide variety of opinions about the discoveries. Nothing we say is set in stone.

Purpose of the sequence

1. Inform: We aim to share our current ideas, thoughts, disagreements, open questions, and any results we have achieved thus far. By openly discussing the complexities and challenges we face, we seek to provide a transparent view of our project's progression and the types of questions we're exploring.
2. Receive Feedback: We invite feedback on our approaches, hypotheses, and findings. Constructive criticism, alternative perspectives, and further suggestions are all welcome.
3. Attract Collaborators: Through this sequence, we hope to resonate with other researchers and practitioners who our exploration appeals to and who are motivated by similar questions. Our goal is to expand our team with individuals who can contribute their unique expertise and insights.

Motivation

We share a general concern regarding the trajectory of Artificial General Intelligence (AGI) development, particularly the risks associated with creating AGI agents designed to maximize objective functions. We have two main concerns:

(I) AGI development might be inevitable

(We assume this concern needs no further justification)

(II) It might be impossible to implement an objective function the maximization of which would be safe

The conventional view on A(G)I agents (see, e.g., Wikipedia) is that they should aim to maximize some function of the state or trajectory of the world, often called a "utility function", sometimes also called a "welfare function". It tacitly assumes that there is such an objective function that can adequately make the AGI behave in a moral way. However, this assumption faces several significant challenges:

• Moral ambiguity: The notion that a universally acceptable, safe utility function exists is highly speculative. Given the philosophical debates surrounding moral cognitivism and moral realism and similar debates in welfare economics, it is possible that there are no universally agreeable moral truths, casting doubt on the existence of a utility function that encapsulates all relevant ethical considerations​​.
• Historical track-record: Humanity's long-standing struggle to define and agree upon universal values or ethical standards raises skepticism about our capacity to discover or construct a comprehensive utility function that safely governs AGI behavior (Outer Alignment)​​ in time.
• Formal specification and Tractability: Even if a theoretically safe and comprehensive utility function could be conceptualized, the challenges of formalizing such a function into a computable and tractable form are immense. This includes the difficulty of accurately capturing complex human values and ethical considerations in a format that can be interpreted and tractably evaluated by an AGI​​.
• Inner Alignment and Verification: Even if such a tractable formal specification of the utility function has been written down, it might not be possible to make sure it is actually followed by the AGI because the specification might be extremely complicated and computationally intractable to verify that the agent's behavior complies with it. The latter is also related to Explainability.

Given these concerns, the implication is clear: AI safety research should spend considerable effort than currently on identifying and developing AGI designs that do not rely on the maximization of an objective function. Given our impression that currently not enough researchers pursue this, we chose to work on it, complementing existing work on what some people call "mild" or "soft optimization", such as Quantilization or Bayesian utility meta-modeling. In contrast to the latter approaches, which are still based on the notion of a "(proxy) utility function", we explore the apparently mostly neglected design alternative that avoids the very concept of a utility function altogether.^[1] The closest existing aspiration-based design we know of is Decision Transformer, which is inherently a learning approach. To complement this, we focus on a planning approach. 

Project history and status

The SatisfIA project is a collaborative effort by volunteers from different programs: AI Safety Camp, SPAR, and interns from different ENS​​s, led by Jobst Heitzig at PIK's Complexity Science Dept. and the FutureLab on Game Theory and Networks of Interacting Agents that has started to work on AI safety in 2023.

Motivated by the above thoughts, two of us (Jobst and Clément) began to investigate the possibility of avoiding the notion of utility function altogether and develop decision algorithms based on goals specified through constraints called "aspirations", to avoid risks from Goodhart's law and extreme actions​​. We originally worked in a reinforcement learning framework, modifying existing temporal difference learning algorithms, but soon ran into issues more related to the learning algorithms than to the aspiration-based policies we actually wanted to study (see Clément's earlier post). 

Because of these issues, discussions at VAISU 2023 and FAR Labs, comments from Stuart Russell, and concepts like davidad's Open Agency Architecture and other safe by design / provably safe approaches, Jobst then switched from a learning framework to a model-based planning framework and adapted the optimal planning algorithms from agentmodels.org to work with aspirations instead, which worked much better and allowed us to focus on the decision making aspect.   

As of spring 2024, the project is participating in AI Safety Camp and SPAR with about a dozen people investing a few hours a week. We are looking for additional collaborators​​. Currently, our efforts focus on theoretical design, prototypical software implementation, and simulations in simple test environments. We will continue documenting our progress in this sequence. We also plan to submit a first academic conference paper soon. ​

Working hypotheses

We use the following working hypotheses during the project, which we ask the reader to adopt as hypothetical premises while reading our text (you don't need to believe them, just assume them to see what might follow from them).

(III) We should not allow the maximization of any function of the state or trajectory of the world

Following the motivation described above, our primary hypothesis posits that it must not be allowed that an AGI aims to maximize any form of objective function that evaluates the state or trajectory of the world in the sense of a proxy utility function. (This does not necessarily rule out that the agent employs any type of optimization of any objective function as part of its decision making, as long as that function is not only a function of the state or trajectory of the world. For example, we might allow some form of constrained maximization of entropy^[2] or minimization of free energy^[2] or the like, which are functions of a probabilistic policy rather than of the state of the world.)

(IV) The core decision algorithm must be hard-coded

The 2nd hypothesis is that to keep an AGI from aiming to maximize some utility function, the AGI agent must use a decision algorithm to pick actions or plans on the basis of the available information, and that decision algorithm must be hard-coded and cannot be allowed to emerge as a byproduct of some form of learning or training process. This premise seeks to ensure that the foundational principles guiding the agent's decision making are known in advance and have verifiable (ideally even provable) properties. This is similar to the "safe by design" paradigm and implies a modular design where decision making and knowledge representation are kept separate. In particular, it rules out monolithic architectures (like using only a single transformer or other large neural network that represents a policy, and a corresponding learning algorithm).

(V) We should focus on model-based planning first and only consider learning later

Although in reality, an AGI agent will never have a perfect model of the world and hence also needs some learning algorithm(s) to improve its imperfect understanding of the world on the basis of incoming data, our 3rd hypothesis is that for the design of the decision algorithm, it is helpful to hypothetically assume in the beginning that the agent already possesses a fixed, sufficiently good probabilistic world model that can predict the consequences of possible courses of action, so that the decision algorithm can choose actions or plans on the basis of these predictions. The rationale is that this "model-based planning" framework is simpler and mathematically more convenient to work with^[3] and allows us to address the fundamental design issues that arise even without learning, before addressing additional issues related to learning. (see also Project history)

(VI) There are useful generic, abstract safety criteria largely unrelated to concrete human values

We hypothesize the existence of generic and abstract safety criteria that can enhance AGI safety in a broad range of scenarios. These criteria focus on structural and behavioral aspects of the agent's interaction with the world, largely independent of the specific semantics or contextual details of actions and states and mostly unrelated to concrete human values. Examples include the level of randomization in decision-making, the degree of change introduced into the environment, the novelty of behaviors, and the agent's capacity to drastically alter world states. Such criteria are envisaged as broadly enhancing safety, very roughly analogous to guidelines such as caution, modesty, patience, neutrality, awareness, and humility, without assuming a one-to-one correspondence to the latter.

(VII) One can and should provide certain guarantees on performance and behavior

We assume it is possible to offer concrete guarantees concerning certain aspects of the AGI's performance and behavior. By adhering to the outlined hypotheses and safety criteria, our aim is to develop AGI systems that exhibit behaviour that is in some essential respects predictable and controlled, reducing risk while fulfilling their intended functions within safety constraints.

(VIII) Algorithms should be designed with tractability in mind, ideally employing Bellman-style recursive formulas

Because the number of possible policies grows exponentially fast with the number of possible states, any algorithm that requires scanning a considerable portion of the policy space (like, e.g., "naive" quantilization over full policies would) soon becomes intractable in complex environments. In optimal control theory, this problem is solved by exploiting certain mathematical features of expected values that allow to make decisions sequentially and compute the relevant quantities (V- and Q-values) in an efficient recursive way using the Hamilton–Jacobi–Bellman equation. Based on our preliminary results, we hypothesize that a very similar recursive approach is possible in our aspiration-based framework in order to keep our algorithms tractable in complex environments. 

Theoretical framework

Agent-environment interface. Our theoretical framework and methodological tools draw inspiration from established paradigms in artificial intelligence (AI), aiming to construct a robust understanding of how agents interact with their environment and make decisions. At the core of our approach is the standard agent–environment interface, a concept that we later elaborate through standard models like (Partially Observed) Markov Decision Processes. For now, we consider agents as entirely separate from the environment — an abstraction that simplifies early discussions, though we acknowledge that the study of agents which are a part of their environment is an essential extension for future exploration.

Simple modular design. To be able to analyse decision-making more clearly, we assume a modular architecture that divides the agent into two main components: the world model and the decision algorithm. The world model represents the agent's understanding and representation of its environment. It encompasses everything the agent knows or predicts about the environment, including how it believes the environment responds to its actions. The decision algorithm, on the other hand, is the mechanism through which the agent selects actions and plans based on its world model and set goals. It evaluates potential actions and their predicted outcomes to choose courses of action that appear safe and aligned with its aspirations.

Studying a modular setup can also be justified by the fact that some leading figures in AI push for modular designs even though current LLM-based systems are not yet modular in this way.

Information theory. For formalizing generic safety criteria, we mostly employ an information theoretic approach, using the mathematically very convenient central concept of Shannon entropy (unconditional, conditional, mutual, directed, etc.) and derived concepts (e.g., channel capacity). This also allows us to compare and combine our findings with approaches based on the free energy principle and active inference. where goals are formulated as desired probability distributions of observations.

High-level structure of studied decision algorithms

The decision algorithms we currently study have the following high-level structure:

1. The agent accepts tasks given as aspirations, i.e., as constraints on the probability distribution of certain task-relevant evaluation metrics. The aspiration will be updated over time in response to achievements, good or bad luck, and other observations.
2. Whenever the agent must decide what the next action is, it performs a number of steps.
   1. First, it uses its world model to estimate what evolutions of the evaluation metrics are still possible from the current state on, and after taking each possible action in the current state. This defines the state's and all possible actions' "feasibility sets".
   2. It then compares each possible action's feasibility set with its current aspiration and decides whether it would have to adjust its aspiration if it were to take that action, and how to adjust its aspiration in that case. This defines all possible actions' "action-aspirations".
   3. It also evaluates all possible actions using one or more safety and performance criteria and picks a combination of one or more candidate actions that appear rather safe.
   4. It then randomizes between these candidate actions in a certain way.
   5. Based on the next observation, it updates its beliefs about the current state.
   6. Finally, in particular when the environment is partially unpredictable and the agent has had some form of good or bad luck, it potentially adjusts its aspiration again ("aspiration propagation").

Depending on the type of aspiration, the details can be designed so that the algorithm comes with certain guarantees about the fulfillment of the goal. 

The next post is about one such simple type of aspiration: aspirations concerning the expected value of a single evaluation metric.

Appendix: Small glossary

This is how we use certain potentially ambiguous terms in this sequence: 

Agent: We employ a very broad definition of "agent" here: The agent is a machine with perceptors that produce observations, and actuators that it can use to take actions, and that uses a decision algorithm to pick actions that it then takes. Think: a household's robot assistant, a firm's or government's strategic AI consultant. We do not assume that the agent has a goal of its own, let alone that it is a maximizer.

Aspiration: A goal formalized via a set of constraints on the state or trajectory or probability distribution of trajectories of the world. E.g., "The expected position of the spaceship in 1 week from now should be the L1 Lagrange point, its total standard deviation should be at most 100 km, and its velocity relative to the L1 point should be at most 1 km/h".

Decision algorithm: A (potentially stochastic) algorithm whose input is a sequence of observations (that the agent's perceptors have made) and whose output is an action (which the agent's actuators then take). A decision algorithm might use a fixed "policy" or a policy it adapts from time to time, e.g. via some form of learning, or some other way of deriving a decision.

Maximizer: An agent whose decision algorithm takes an objective function and uses an optimization algorithm to find the (typically unique) action at which the predicted expected value of the objective function (or some other summary statistic of the predicted probability distribution of the values of this function) is (at least approximately) maximal^[4], and then outputs that action.

Optimization algorithm: An algorithm that takes some function $f$  (given as a formula or as another algorithm that can be used to compute values $f\left(x\right)$ of that function), calculates or approximates the (typically unique) location $x$ of the global maximum (or minimum) of $f$, and returns that location $x$. In other words: an algorithm $O:f\mapsto O\left(f\right)\approx \arg {max}_{x}f\left(x\right)$.

Utility function: A function (only defined up to positive affine transformations) of the (predicted) state of the world or trajectory of states of the world that represents the preferences of the holder of the utility function over all possible probability distributions of states or trajectories of the world in a way conforming to the axioms of expected utility theory or some form of non-expected utility theory such as cumulative prospect theory.

Loss function: A non-negative function of potential outputs of an algorithm (actions, action sequences, policies, parameter values, changes in parameters, etc.) that is meant to represent something the algorithm shall rather keep small.

Goal: Any type of additional input (additional to the observations) to the decision algorithm that guides the direction of the decision algorithm, such as: 

• a desirable state of the world or trajectory of states of the world, or probability distribution over trajectories of states of the world, or expected value for some observable
• a (crisp or fuzzy) set of acceptable states, trajectories, distributions of such, or expected value of some observable
• a utility function for expected (or otherwise aggregated) utility maximization 

Planning: The activity of considering several action sequences or policies ("plans") for a significant planning time horizon, predicting their consequences using some world model, evaluating those consequences, and deciding on one plan the basis of these evaluations.

Learning: Improving one's beliefs/knowledge over time on the basis of some stream of incoming data, using some form of learning algorithm, and potentially using some data acquisition strategy such as some form of exploration. 

Satisficing: A decision-making strategy that entails selecting an option that meets a predefined level of acceptability or adequacy rather than optimizing for the best possible outcome. This approach emphasizes practicality and efficiency by prioritizing satisfactory solutions over the potentially exhaustive search for the optimal one. See also the satisficer tag.

Quantilization: A technique in decision theory, introduced in a 2015 paper by Jessica Taylor. Instead of selecting the action that maximizes expected utility, a quantilizing agent chooses randomly among the actions which rank higher than a predetermined quantile in some base distribution of actions. This method aims to balance between exploiting known strategies and exploring potentially better but riskier ones, thereby mitigating the impact of errors in the utility estimation. See also the quantilization tag.

Reward Function Regularization: A method in machine learning and AI design where the reward function is modified by adding penalty terms or constraints to discourage certain behaviors or encourage others, such as in Impact Regularization. This approach is often used to incorporate safety, ethical, or other secondary objectives into the optimization process. As such, it can make use of the same type of safety criteria as an aspiration-based algorithm might.

Safety Criterion: A (typically quantitative) formal criterion that assesses some potentially relevant safety aspect of a potential action or plan. E.g., how much change in the world trajectory could this plan maximally cause? Safety criteria can be used as the basis of loss functions or in reward function regularization to guide behavior.  

Using Aspirations as a Means to Maximize Reward: An approach in adaptive reinforcement learning where aspiration levels (desired outcomes or benchmarks) are adjusted over time based on performance feedback. Here, aspirations serve as dynamic targets to guide learning and action selection towards ultimately maximizing cumulative rewards. This method contrasts with using aspirations as fixed goals, emphasizing their role as flexible benchmarks in the pursuit of long-term utility optimization. This is not what we assume in this project, where we assume no such underlying utility function.

Acknowledgements

In addition to AISC, SPAR, VAISU, FAR Labs, and GaNe, we'd like to thank everyone who contributed or continues to contribute to the SatisfIA project for fruitful discussions and helpful comments and suggestions. 

1. ^{^}

   This might not be trivial of course if the agent might "outsource" or otherwise cause the maximization of some objective function by others, a question that is related to "reflective stability" in the sense of this post. An rule additional  "do not maximize" would hence be something like "do not cause maximization by other agents", but this is beyond the scope of the project at the moment.

2. ^{^}

   Information-theoretic, not thermodynamic.

3. ^{^}

   This is also why Sutton and Barto's leading textbook on RL starts with model-based algorithms and turns to learning only in chapter 6.

4. ^{^}

   That the algorithm uses an optimization algorithm that it gives the function to maximize to is crucial in this definition. Without this condition, every agent would be a maximizer, since for whatever output $a$ the decision algorithm produces, one can always find ex post some function $f$ for which $\arg {max}_{x}f\left(x\right)=a$.