Subjective functions

We present a formal process to enable non-experts to instantiate and iterate on human-aligned reward functions, i.e. reward functions that adhere to a given preference ordering over trajectories. Given a task described in natural language, our process produces a linear reward function in three steps: distill the task's objectives into a set of fundamental objectives and derive measurable outcome variables that capture those fundamental objectives, select a causally representative subset of outcome variables as the reward terms, and fit weights to those reward terms via preference elicitation. Our contributions describe the first step and formalize the latter two steps. The first is a guided workflow for deriving outcome variables. The second is a reduction of reward term selection to minimum-cost partial cover on a causal DAG, solved in polynomial time via max-flow. The third is a geometric framing of weight fitting as a convex feasibility problem iteratively narrowed by preference queries, solved by existing separation oracle methods. To the best of our knowledge, this is the first reward-design method that maintains a deterministically conflict-free feasible weight region, narrowed to a desired tolerance via a separation oracle with O(n log κ) preference queries.

Frontier AI systems perform best in settings with clear, stable, and verifiable objectives, such as code generation, mathematical reasoning, games, and unit-test-driven tasks. They remain less reliable in open-ended settings, including scientific assistance, long-horizon agents, high-stakes advice, personalization, and tool use, where the relevant objective is ambiguous, context-dependent, delayed, or only partially observable. We argue that many such failures are not merely failures of scale or capability, but failures of objective selection: the system optimizes a locally visible signal while missing which objectives should govern the interaction. We formulate this problem as \emph{contextual multi-objective optimization}. In this setting, systems must consider multiple, context-dependent objectives, such as helpfulness, truthfulness, safety, privacy, calibration, non-manipulation, user preference, reversibility, and stakeholder impact, while determining which objectives are active, which are soft preferences, and which must function as hard or quasi-hard constraints. These examples are not intended as an exhaustive taxonomy: different domains and deployment settings may activate different objective dimensions and different conflict-resolution procedures. Our framework models AI behavior as a context-dependent choice rule over candidate actions, objective estimates, active constraints, stakeholders, uncertainty, and conflict-resolution procedures. We outline an implementation pathway based on decomposed objective representations, context-to-objective routing, hierarchical constraints, deliberative policy reasoning, controlled personalization, tool-use control, diagnostic evaluation, auditing, and post-deployment revision.

I discuss some quantitative representations of Promise Theory for processes involving autonomous agents. Agent models are common in software systems, machine learning, and biology, for example, but may also apply to physics and other forms of engineering. I describe how Bayesian probability and information theoretic optimization, including Active Inference, may be incorporated with promise semantics -- as well as how Promise Theory supplements solutions, helping to avoid probability's pitfalls, which include non-local coordination, calibrating, and normalizing probabilistic computations. The role of boundary conditions in constraining allowed states and selecting decision thresholds is a form of promise, and agent alignment provides a scalable definition of intent. Autonomous agents may congeal into swarms with superagent characteristics by trying to minimize their information, despite uncertainty that works to maximize it. The use of Promise Theory involves some research challenges as well as stylistic preferences.