Monotonicity of value function and optimal policy in cross-layer design of communication systems
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Bibliographic record
Abstract
Markov decision theory has been widely used to model engineering setups as sequential optimization problems.Using Markov decision models and underling techniques in this theory let the engineers improve the performance of the system.Dynamic programming and approximate dynamic programming are the main tools to find optimal policies; however, just finding the optimal policy numerically does not add anything to our engineering intuition about the physical system.In order to grasp a deeper understanding of the underlying physical process, designer is interested in investigating qualitative properties of the optimal value function and optimal policy.These qualitative results not only help researchers to understand the behavior of the physical system better, but also let designers simplify their implementation.Knowing the structure of optimal policy can reduce the implementation of an optimal policy from a look up table to a sparse matrix or just set of thresholds.Markov decision theory has been widely used in queuing problems related to communication systems.In these problems a transmitter is dealing with transmitting a stream of data packets queued in a buffer, over a physical channel.Transmitter should not only deal with stochasticity in the arriving data but also it should manage the physical layer constraints.These type of problems usually are categorized as queuing problems, and in the literature, the solution to these problems are investigated with tools in both queuing theory and Markov decision theory.In this thesis, our emphasis is on investigating monotonicity property of the optimal strategy in such models.We start with brief introduction to Markov decision processes and common techniques and tools in Markov decision theory to prove monotonicity.We then investigate a classic result in this area.We present simpler proofs for the existing results and try to generalize the idea in two directions.First, we try to establish monotonicity property when transmitter has access to an ACK/NACK feedback channel.In the second approach, we try to show these properties in an energy harvesting scenario.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.003 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it