11. r
m
F(t)
k
y(t)
y = displacement
F = force applied
m = mass of the block
r = damping constant
k = spring constant
12. Using Newton’s second law F (t ) = my ' ' (t )
◦ Spring force: f1 = ky (t ) r
◦ Damping force: f 2 = ry ' (t )
m
F(t)
This gives the equation k
y(t)
F (t ) = ky (t ) + ry ' (t )
13. r
F(t)
k
y(t)
F (t ) = ky (t ) + ry ' (t )
y = performance
F = number of training samples
k = constant related to the new training samples
r = constant related to the change in the new training samples
14. Generate an input signal
Log-normal random walk to
add noise
Maximum likelihood
estimation
16. Controlled Recommender System
Controller
Manipulated Variable
Control control (e.g., number of
input Actuator new training samples)
Function
Dynamics
error
+- Monitor
Performance variable
Reference
performance
17. Reference Value Disturbance
yr (t ) e(t ) = yr (t ) − y (t ) n(t )
+
e(t ) u (t ) Performance
∑ Controller
Dynamics
Rec. Error Control
y (t )
- Signal
y (t ) Rec.
Accuracy
Measurement
20. Type Rise time Settling time Overshoot (%)
(sec) (sec)
P 5 10 0
PD 1 5 8.21
PI 0 10 36.8
PID 0 10 15.7
P controller PD controller PI controller PID controller
22. Simulate system for 30 days (once a day)
3 reference values (RMSE 0.95, 0.9, 0.86)
Measure
◦ Settling time
◦ Error (with respect to reference) – RMSE-SS
◦ Stability (with respect to reference) – SD-SS
◦ Overshoot
23. Type Settling RMSE-SS SD-SS Overshoot
time (error) (stability) (%)
P (0.86) 23 0.0104 0.0034 0
PD (0.86) 20.8 0.0059 0.0037 0.18
PI (0.86) 18.6 0.0055 0.0047 0.49
PID (0.86) 18.6 0.0045 0.0045 0.72
PD controller
24. Type Settling RMSE-SS SD-SS Overshoot
time (error) (stability) (%)
P 20 0.0068 0.0052 0.50
PD 18.8 0.0054 0.0055 0.98
PI 20.6 0.0137 0.0075 2.50
PID 17.8 0.0091 0.0059 1.86
P controller PD controller PI controller PID controller
25. Computation Performance loss Computational gain
26. Fixed computational cost would also fix
update frequency (given the resources
available)
System can provide regular updates
independent from the rate of the new
samples
Resources are used to their limits (e.g. EC2)
27. RECOMMENDATION
recommendation
SERVER
usage data
RECOMMENDER
INPUT CONTROLLER feedback
TRAINING DATA
PROCESSOR
RECOMMENDATION request data
ASSESSOR
USAGE DATA
PROCESSOR
28. Certain aspects of the system are to be
controlled
Stability and predictability are important
Use resources to their limits
29. Optimise rather than stabilise over time
Obtain system dynamics
Describe objective to be achieved (finite or
infinite horizon)
30. Describe system dynamics
Design a feedback loop
Evaluate control system on real data
Most of the time systems is viewed and evaluated in a static context Snapshot at time t How the system evolves Items are changing People are changing Change the outcome
Understand the system dynamics Select important aspects of the system Gain control over certain objectives
Understand and describe system -> predict over time Example: we know the system at time t, we know the change, we know what it will be at t+1 Organise resources accordingly Controlling the system brings stability
Describe Select Build feedback Add controller Test
Performance loss is calculated with respect to training four times a day. Red line twice a day – midnight and midday Blue line once a day – only at midnight
Use all and train whenever you can Part of data would give more frequent and regular updates
the relationship between the number of training samples and the overall performance Number of training samples related to performance Gain control performance
Balance the mass to keep the distance from the wall constant Pull and release
The acceleration a of a body is parallel and directly proportional to the net force F and inversely proportional to the mass m First order differential equation
The analogy to recommender systems is that Y is the performance of the system K – new training samples R – change in new training samples
Explain input and put through a recsys for 30 days Three scenarios, new data samples are increasing, deceasing and stable (showing the increasing one). Learn parameter R-squared, the coefficient of determination, to measure the accuracy of the prediction.
General concept Dynamics
Three components
Rise time Settling time Overshoot – maximum percentage the system might go over the reference
Based on analysis Picked to get the fastest rise time Rise time – PI, PID Overshoot – PI, PID not really good PD is the best
Analysis and results are consistent Settling time – best PI and PID Overshoot – highest for PID and PI P is zero Overall PD has the best properties
Reduce performance would reduce computation Red line – performance loss, computational gain Blue line – performance loss, computational gain once the required performance has reached, the computational cost becomes stable.
EC2 pay per instance, use it all but keep regular updates
How it works now - subscription and purchase is used Data that can be collected – PVR recording logs, subscription packages, purchase data, live TV watch, Facebook shares, content information Identify the usefulness of the signal per user basis Enhance recommendation by requesting additional information Reduce data and computation
Certain aspects – need to fix aspects of the system Stability would bring predictability More optimal resource allocation
First two steps are similar Example here – optimise performance over time Can be used for cold start problem Good quality recommendation from the beginning
Sequence of design Dynamics – feedback loop (analytical) Put into production – evaluate on real data Plug-in different dynamics and different controllers
