Trajectory Generation as a Markov Decision Process
The process of generating a sequence, or trajectory (τ), can be formally modeled as a Markov Decision Process (MDP). This framework is essential for applying reinforcement learning to sequential tasks, as it defines the states, actions, and transition probabilities that govern the generation of trajectories under a given policy.
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Ch.4 Alignment - Foundations of Large Language Models
Foundations of Large Language Models
Foundations of Large Language Models Course
Computing Sciences
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Objective Function as Expected Cumulative Reward (Performance Function)
An agent operates in an environment where sequences of events unfold over time. The agent's behavior is described by a policy, denoted as π(a|s), which gives the probability of taking action 'a' when in state 's'. The environment's dynamics are described by a transition function, P(s'|s, a), which gives the probability of moving to the next state 's'' after taking action 'a' in state 's'. The process begins from an initial state, s₀, with a probability of P(s₀).
Consider the following specific two-step sequence of events (a trajectory):
- The process starts in state s₀.
- The agent takes action a₀.
- The environment transitions to state s₁.
- The agent takes action a₁.
- The environment transitions to state s₂.
Which expression correctly represents the probability of this entire specific trajectory occurring?
Diagnosing a Faulty Sequence Generation Process
When modeling the generation of a sequence of states and actions as a Markov Decision Process, the probability of transitioning to a new state at any given step depends on the complete history of all states and actions that have occurred since the beginning of the sequence.
Notational Variations in State-Action Sequences (Trajectories)
An agent is generating a sequence by interacting with an environment. For a single time step, starting from state
s_t, arrange the following events in the correct logical order.