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35 lines
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2.2 KiB
Markdown
35 lines
No EOL
2.2 KiB
Markdown
---
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type: claim
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domain: internet-finance
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description: "Small state spaces enable exact value iteration while large spaces require approximate policies"
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confidence: likely
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source: "Li et al., 'An Overview for Markov Decision Processes in Queues and Networks' (2019)"
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created: 2026-03-11
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---
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# Pipeline state space size determines whether exact MDP solution or threshold heuristics are optimal
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The curse of dimensionality in queueing MDPs creates a sharp divide in optimal solution approaches. Systems with manageable state spaces—such as pipelines with queue depths across 3 stages, worker counts, and time-of-day variables—can use exact MDP solution via value iteration to derive provably optimal policies.
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However, as state space grows (multiple queues, many stages, complex dependencies), exact solution becomes computationally intractable. For these systems, approximate dynamic programming or reinforcement learning becomes necessary, accepting near-optimal performance in exchange for tractability.
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The Teleo pipeline architecture sits in the tractable regime: queue depths across 3 stages, worker counts, and time-of-day create a state space small enough for exact solution. This means the system can compute provably optimal policies rather than relying on heuristics, though the threshold structure of optimal policies means well-tuned simple rules would also perform near-optimally.
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## Evidence
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Li et al. identify curse of dimensionality as the key challenge: "state space explodes with multiple queues/stages." The survey distinguishes between:
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- Small state spaces: exact MDP solution via value iteration
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- Large state spaces: approximate dynamic programming, reinforcement learning
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Practical approaches for large systems include deep RL for queue management in networks and cloud computing, accepting approximation in exchange for scalability.
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The source explicitly notes that Teleo pipeline has "a manageable state space (queue depths across 3 stages, worker counts, time-of-day)—small enough for exact MDP solution via value iteration."
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---
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Relevant Notes:
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- optimal queue policies have threshold structure making simple rules near-optimal
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- domains/internet-finance/_map
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Topics:
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- domains/internet-finance/_map |