The second part of our series on Foundations of Algorithmic Decision Making continues with the Five Regions of Decision Complexity—a framework to help map uncertainty to the right decision-making approach.

Foundations of Algorithmic Decision Making: The Five Regions of Decision Complexity

We make decisions all the time, but not all decisions are alike. Consider the following situations:

• Reasoning: About uncertainty and objectives at a single point in time.
• Sequential: Making a sequence of decisions while observing outcomes as we proceed.
• Learning: Acting in an environment where the model is unknown and must be learned through interaction.
• Imperfect Information: Where the full state of the environment is not observable.
• Multi-Agent: Making decisions in environments shared with multiple agents.

Before diving into examples, let’s take a bird’s‑eye view of the landscape. Think of these five regions as different colors on a canvas. When faced with a problem, we can look toward the region whose “color” best matches the nature of the uncertainty we’re dealing with.

Regions of Decision Making

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Region 1 — Single‑step uncertainty

Here, uncertainty is represented using probability distributions. The key questions are:

• How do we construct these models?
• How do we use them to make inferences?
• How do we learn their parameters and structure?

This is where utility theory and decision networks come into play.

Region 2 — Sequential decisions

In this region, we must reason about future sequences of actions and observations. Outcomes are uncertain, and the agent must plan ahead. The formulation depends heavily on:

• What the agent knows about the model
• How observable the environment is

The standard mathematical framework here is the Markov Decision Process (MDP).

Region 3 — Learning the model

Here, the dynamics and rewards are not known in advance. The agent must:

• Balance exploration (trying new actions) with exploitation (using what it has learned).
• Assign credit to earlier decisions that lead to later rewards.
• Generalize from limited experience.

This is the domain of Reinforcement Learning (RL).

Region 4 — Imperfect state information

In this region, the agent cannot observe the true state directly. Instead, it receives observations that are probabilistically related to the underlying state. The agent maintains a belief distribution over possible states and updates it as it acts.

A policy maps beliefs to actions, and this framework is captured by the Partially Observable Markov Decision Process (POMDP).

Region 5 — Multiple agents

Here, several agents act simultaneously in a shared environment. The uncertainty comes from the state, the actions of other agents, and the stochastic transitions. Relevant models include:

• Markov Games (MG)
• Partially Observable Markov Games (POMG)
• Decentralized POMDPs (Dec‑POMDPs)

As the next step in our journey, we will explore each of these regions with concrete examples. Stay tuned!

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